Abstract
This chapter gives a general overview of the fuzzy model-based control which covers the background, literature review, development of the field, fuzzy models, fuzzy control methodologies, stability analysis approaches and control problems. The motivation of moving from basic fuzzy logic system for automatic control to fuzzy model-based control is first discussed. It follows by discussing various types of fuzzy models such as T–S and polynomial fuzzy models. Various types of fuzzy controllers are reviewed and their characteristics are discussed. Combining various fuzzy models and fuzzy controllers, a wide range of fuzzy model-based control systems are formed. Stability analysis of the fuzzy model-based control systems subject to various types of Lyapunov functions, types of stability analysis and types of stability analysis techniques are gone through. The characteristics of the three main types of control problems including stabilization, regulation and tracking are discussed.
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References
Mendel, J.M.: Fuzzy logic systems for engineering: a tutorial. Proc. IEEE 83(3), 345–377 (1995)
Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man-Mach. Stud. 7(1), 1–13 (1975)
Mamdani, E.H.: Advances in the linguistic synthesis of fuzzy controllers. Int. J. Man-Mach. Stud. 8(6), 669–678 (1976)
Kickert, W.J.M., Mamdani, E.H.: Analysis of a fuzzy logic controller. Fuzzy Sets Syst. 1(1), 29–44 (1978)
Tong, R.M., Beck, M.B., Latten, A.: Fuzzy control of the activated sludge wastewater treatment process. Automatica 16(6), 695–701 (1980)
Holmblad, L.P., Ostergaard, J.J.: Control of a cement kiln by fuzzy logic techniques. In: Proceedings of Conference 8-th IFAC, pp. 809–814. Kyoto, Japan (1981)
Feng, G.: A survey on analysis and design of model-based fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(5), 676–697 (2006)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modelling and control. IEEE Trans. Syst. Man. Cybern. smc-15(1), 116–132 (1985)
Sugeno, M., Kang, G.T.: Structure identification of fuzzy model. Fuzzy Sets Syst. 28(1), 15–33 (1988)
Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)
Wang, H.O., Tanaka, K., Griffin, M.F.: An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans. Fuzzy Syst. 4(1), 14–23 (1996)
Tanaka, K., Ikeda, T., Wang, H.O.: Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs. IEEE Trans. Fuzzy Syst. 6(2), 250–265 (1998)
Tanaka, K., Yoshida, H., Ohtake, H., Wang, H.O.: A sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems. IEEE Trans. Fuzzy Syst. 17(4), 911–922 (2009)
Tanaka, K., Ohtake, H., Wang, H.O.: Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach. IEEE Trans. Syst. Man Cybern. - Part B: Cybern. 39(2), 561–567 (2009)
Sala, A., Ariño, C.: Polynomial fuzzy models for nonlinear control: a Taylor-series approach. IEEE Trans. Fuzzy Syst. 17(6), 284–295 (2009)
Tanaka, K., Iwasaki, M., Wang, H.O.: Switching control of an R/C hovercraft: stabilization and smooth switching. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 31(6), 853–863 (2001)
Lam, H.K., Leung, F.H.F., Lai, J.C.Y.: Fuzzy model-based control systems using fuzzy combination techniques. Int. J. Fuzzy Syst. 9(3), 123–132 (2007)
Cao, Y.Y., Frank, P.M.: Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst. 8(2), 200–211 (2000)
Cao, Y.Y., Frank, P.M.: Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models. Fuzzy Sets Syst. 124(2), 213–229 (2001)
Wang, R.J., Lin, W.W., Wang, W.J.: Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34(2), 1288–1292 (2004)
Gao, H., Liu, X., Lam, J.: Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 39(2), 306–317 (2009)
Qiu, J., Feng, G., Yang, J.: A new design of delay-dependent robust filtering for discrete-time T-S fuzzy systems with time-varying delay. IEEE Trans. Fuzzy Syst. 17(5), 1044–1058 (2009)
Chen, B., Liu, X., Lin, C., Liu, K.: Robust H\(_\infty \) control of Takagi-Sugeno fuzzy systems with state and input time delays. Fuzzy Sets Syst. 160(4), 403–422 (2009)
Zhang, B., Xu, S.: Delay-dependent robust H\(_\infty \) control for uncertain discrete-time fuzzy systems with time-varying delays. IEEE Trans. Fuzzy Syst. 17(4), 809–823 (2009)
Dong, H., Wang, Z., Ho, D.W.C., Gao, H.: Robust H\(_\infty \) fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements. IEEE Trans. Fuzzy Syst. 18(4), 712–725 (2010)
Wu, L., Su, X., Shi, P., Qiu, J.: A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 41(1), 273–286 (2011)
Dong, H., Wang, Z., Lam, J., Gao, H.: Fuzzy model-based robust fault detection with stochastic mixed time delays and successive packet dropouts. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 42(2), 365–376 (2012)
Tsai, S.H., Sun, C., Lo, J.C., Lam, H.K.: Relaxed stabilization of T-S fuzzy systems with time-delay. In: Proceedings of the 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2013), pp. 1–6. IEEE (2013)
Peng, C., Fei, M.R.: An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay. Fuzzy Sets Syst. 212, 97–109 (2013)
Balasubramaniam, P., Senthilkumar, T.: Delay-dependent robust stabilization and H\(_\infty \) control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays. Int. J. Autom. Comput. 10(1), 18–31 (2013)
Zhao, L., Gao, H., Karimi, H.R.: Robust stability and stabilization of uncertain T-S fuzzy systems with time-varying delay: an input-output approach. IEEE Trans. Fuzzy Syst. 21(5), 883–897 (2013)
Kchaou, M., Souissi, M., Toumi, A.: Delay-dependent stability and robust L\(_2\) - L\(_\infty \) control for a class of fuzzy descriptor systems with time-varying delay. Int. J. Robust Nonlinear Control 23(3), 284–304 (2013)
Chen, W.H., Wei, D., Zheng, W.X.: Delayed impulsive control of Takagi-Sugeno fuzzy delay systems. IEEE Trans. Fuzzy Syst. 21(3), 516–526 (2013)
Wu, L., Yang, X., Lam, H.K.: Dissipativity analysis and synthesis for discrete-time T-S fuzzy stochastic systems with time-varying delay. IEEE Trans. Fuzzy Syst. 22(2), 380–394 (2014)
Yang, X., Wu, L., Lam, H.K., Su, X.: Stability and stabilization of discrete-time T-S fuzzy systems with stochastic perturbation and time-varying delay. IEEE Trans. Fuzzy Syst. 22(1), 124–138 (2014)
Gassara, H., Hajjaji, A.E., Kchaou, M., Chaabane, M.: Robust H\(_\infty \) reliable control of time delay nonlinear systems via Takagi-Sugeno fuzzy models. Int. J. Syst. Sci. 45(3), 667–681 (2014)
Tsai, S.H.: Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input. Int. J. Syst. Sci. 45(3), 187–201 (2014)
Li, F., Shi, P., Wu, L., Zhang, X.: Fuzzy model-based \({\cal D}\)-stability and nonfragile control for discrete-time descriptor systems with multiple delays. IEEE Trans. Fuzzy Syst. 22(4), 1019–1025 (2014)
Li, H., Jing, X., Karimi, H.: Output-feedback based H\(_\infty \) control for active suspension systems with control delay. IEEE Trans. Ind. Electron. 61(1), 436–446 (2014)
Souza, F.O., Campos, V.C.S., Palhares, R.M.: On delay-dependent stability conditions for Takagi-Sugeno fuzzy systems. J. Frankl. Inst. 351(7), 3707–3718 (2014)
Li, H., Gao, Y., Wu, L., Lam, H.K.: Fault detection for T-S fuzzy time-delay systems: Delta operator and input-output methods. IEEE Trans. Cybern. 45(2), 229–241 (2015)
Liang, Q., Mendel, J.M.: Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters. IEEE Trans. Fuzzy Syst. 8(5), 551–563 (2000)
Lam, H.K., Seneviratne, L.D.: Stability analysis of interval type-2 fuzzy model-based control systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(3), 617–628 (2008)
Lam, H.K.: LMI-based stability analysis for fuzzy model-based control systems using artificial T-S fuzzy model. IEEE Trans. Fuzzy Syst. 19(3), 505–513 (2011)
Lam, H.K., Li, H., Deters, C., Secco, E., Wurdemann, H.A., Althoefer, K.: Control design for interval type-2 fuzzy systems under imperfect premise matching. IEEE Trans. Ind. Electron. 61(2), 956–968 (2014)
Sheng, L., Ma, X.: Stability analysis and controller design of interval type-2 fuzzy systems with time delay. Int. J. Syst. Sci. 45(5), 977–993 (2014)
Sheng, L., Ma, X.: Stability analysis and controller design of discrete interval type-2 fuzzy systems. Asian J. Control 16(4), 1091–1104 (2014)
Chen, C.L., Chen, P.C., Chen, C.K.: Analysis and design of fuzzy control system. Fuzzy Sets Syst. 57(2), 125–140 (1993)
Wang, W.J., Yan, S.F., Chiu, C.H.: Flexible stability criteria for a linguistic fuzzy dynamic system. Fuzzy Sets Syst. 105(1), 63–80 (1999)
Kim, E., Lee, H.: New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE Trans. Fuzzy Syst. 8(5), 523–534 (2000)
Liu, X., Zhang, Q.: New approaches to H\(_\infty \) controller designs based on fuzzy observers for Takagi-Sugeno fuzzy systems via LMI. Automatica 39(9), 1571–1582 (2003)
Liu, X., Zhang, Q.: Approaches to quadratic stability conditions and H\(_\infty \) control designs for Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 11(6), 830–839 (2003)
Teixeira, M.C.M., Assuncão, E., Avellar, R.G.: On relaxed LMI-based designs for fuzzy regulators and fuzzy observers. IEEE Trans. Fuzzy Syst. 11(5), 613–623 (2003)
Fang, C.H., Liu, Y.S., Kau, S.W., Hong, L., Lee, C.H.: A new LMI-based approach to relaxed quadratic stabilization of Takagi-Sugeno fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(3), 386–397 (2006)
Sala, A., Ariño, C.: Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya’s theorem. Fuzzy Sets Syst. 158(24), 2671–2686 (2007)
Montagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D.: Convergent LMI relaxations for quadratic stabilizability and control of Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 17(4), 863–873 (2009)
Lo, J.C., Wan, J.R.: Studies on linear matrix inequality relaxations for fuzzy control systems via homogeneous polynomials. IET Control Theory Appl. 4(11), 2293–2302 (2010)
Chadli, M., Karimi, H.R., Shi, P.: On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems. J. Frankl. Inst. 351(3), 1453–1463 (2014)
Hu, X., Wu, L., Hu, C., Wang, Z., Gao, H.: Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach. Int. J. Syst. Sci. 45(8), 1740–1756 (2014)
Li, H., Wu, C., Feng, Z.: Fuzzy dynamic output-feedback control of non-linear networked discrete-time system with missing measurements. IET Control Theory Appl. 9(3), 327335 (2015)
Chung, H.Y., Wu, S.M., Yu, F.M., Chang, W.J.: Evolutionary design of static output feedback controller for Takagi-Sugeno fuzzy systems. IET Control Theory Appl. 1(4), 1096–1103 (2007)
Kau, S.W., Lee, H.J., Yang, C.M., Lee, C.H., Hong, L., Fang, C.H.: Robust H\(_\infty \) fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties. Fuzzy Sets Syst. 158(2), 135–146 (2007)
Huang, D., Nguang, S.K.: Static output feedback controller design for fuzzy systems: an ILMI approach. Inf. Sci. 177(14), 3005–3015 (2007)
Li, J., Wang, H., Niemann, D., Tanaka, K.: Dynamic parallel distributed compensation for Takagi-Sugeno fuzzy systems: An LMI approach. Inf. Sci. 123(3–4), 201–221 (2000)
Lam, H.K., Leung, F.H.F.: Stability analysis of fuzzy control systems subject to uncertain grades of membership. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 35(6), 1322–1325 (2005)
Ariño, C., Sala, A.: Extensions to “stability analysis of fuzzy control systems subject to uncertain grades of membership”. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(2), 558–563 (2008)
Lam, H.K., Narimani, M.: Stability analysis and performance design for fuzzy model-based control system under imperfect premise matching. IEEE Trans. Fuzzy Syst. 17(4), 949–961 (2009)
Lam, H.K., Narimani, M.: Quadratic stability analysis of fuzzy model-based control systems using staircase membership functions. IEEE Trans. Fuzzy Syst. 18(1), 125–137 (2010)
Lam, H.K., Narimani, M.: Sum-of-squares-based stability analysis of polynomial fuzzy model-based control systems. In: Proceedings of 2009 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2009), pp. 234–239. IEEE, ICC Jeju, Jeju Island, Korea (2009)
Lam, H.K., Seneviratne, L.D.: Stability analysis of polynomial fuzzy model-based control systems under perfect/imperfect premise matching. IET Control Theory Appl. 5(15), 1689–1697 (2011)
Lam, H.K.: Polynomial fuzzy model-based control systems: Stability analysis via piecewise-linear membership functions. IEEE Trans. Fuzzy Syst. 19(3), 588–593 (2011)
Lam, H.K.: Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy model-based control approach. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 41(1), 258–267 (2012)
Li, H., Sun, X., Shi, P., Lam, H.K.: Control design of interval type-2 fuzzy systems with actuator fault: Sampled-data control approach. Inf. Sci. 32, 1–13 (2015)
Zhou, Q., Liu, D., Gao, Y., Lam, H.K., Sakthivel, R.: Interval type-2 fuzzy control for nonlinear discrete-time systems with time-varying delays. Neurocomputing 157, 22–32 (2015)
Han, Z.X., Feng, G., Walcott, B.L., Ma, J.: Dynamic output feedback controller design for fuzzy systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 30(1), 204–210 (2000)
Chen, B.S., Tseng, C.S., Uang, H.J.: Mixed H\(_2\)/H\(_\infty \) fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach. IEEE Trans. Fuzzy Syst. 8(3), 249–265 (2000)
Lo, J.C., Lin, M.L.: Robust H\(_\infty \) nonlinear control via fuzzy static output feedback. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 50(11), 1494–1502 (2003)
Chang, W., Park, J.B., Joo, Y.H., Chen, G.: Static output-feedback fuzzy controller for Chen’s chaotic system with uncertainties. Inf. Sci. 151, 227–244 (2003)
Nguang, S.K., Shi, P.: H\(_\infty \) fuzzy output feedback control design for nonlinear systems: An LMI approach. IEEE Trans. Fuzzy Syst. 11(3), 331–340 (2003)
Nguang, S.K., Shi, P.: Fuzzy output feedback control of nonlinear systems under sampled measurements. Automatica 39(12), 2169–2174 (2003)
Xu, S., Lam, J.: Robust H\(_\infty \) control for uncertain discrete-time-delay fuzzy systems via output feedback controllers. IEEE Trans. Fuzzy Syst. 13(1), 82–93 (2005)
Huang, D., Nguang, S.K.: Robust H\(_\infty \) static output feedback control of fuzzy systems: An ILMI approach. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 36(1), 216–222 (2006)
Assawinchaichote, W., Nguang, S.K.: Fuzzy H\(_\infty \) output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach. IEEE Trans. Fuzzy Syst. 14(3), 361–371 (2006)
Mansouri, B., Manamanni, N., Guelton, K., Kruszewski, A., Guerra, T.M.: Output feedback LMI tracking control conditions with H\(_\infty \) criterion for uncertain and disturbed TS models. Inf. Sci. 179(4), 446–457 (2009)
Lian, K.Y., Liou, J.J.: Output tracking control for fuzzy systems via output feedback design. IEEE Trans. Fuzzy Syst. 14(5), 628–639 (2006)
Guelton, K., Bouarar, T., Manamanni, N.: Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems - a descriptor redundancy approach. Fuzzy Sets Syst. 160(19), 2796–2811 (2009)
Lee, K.R., Kim, J.H., Jeung, E.T., Park, H.B.: Output feedback robust H\(_\infty \) control of uncertain fuzzy dynamic systems with time-varying delay. IEEE Trans. Fuzzy Syst. 8(6), 657–664 (2000)
Li, H., Chen, B., Zhou, Q., Qian, W.: Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans. on Syst., Man and Cybern., Part B: Cybern. 39(1), 94–102 (2009)
Wu, L., Zheng, W.X.: L\(_2\) - L\(_\infty \) control of nonlinear fuzzy Itô stochastic delay systems via dynamic output feedback. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 39(5), 1308–1315 (2009)
Tognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D.: Reduced-order dynamic output feedback control of continuous-time T-S fuzzy systems. Fuzzy Sets Syst. 207, 27–44 (2012)
Kim, D.W., Lee, H.J.: Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: exact discrete-time design approach. Fuzzy Sets Syst. 201, 20–39 (2012)
Qiu, J., Feng, G., Gao, H.: Static-output-feedback control of continuous-time T-S fuzzy affine systems via piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 21(2), 245–261 (2013)
Krokavec, D., Filasová, A.: Stabilizing fuzzy output control for a class of nonlinear systems. Adv. Fuzzy Syst. 2013, 1 (2013)
Liu, Y., Ban, X., Wu, F., Lam, H.K.: Dynamic output feedback controller design for T-S fuzzy plants with actuator saturation using linear fractional transformation. In: Proceedings of the 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2014), pp. 2125–2132. IEEE (2014)
Ma, X.J., Sun, Z.Q., He, Y.Y.: Analysis and design of fuzzy controller and fuzzy observer. IEEE Trans. Fuzzy Syst. 6(1), 41–51 (1998)
Lian, K.Y., Chiu, C.S., Chiang, T.S., Liu, P.: LMI-based fuzzy chaotic synchronization and communications. IEEE Trans. on Fuzzy Systems 9(4), 539–553 (2001)
Lian, K.Y., Chiu, C.S., Chiang, T.S., Liu, P.: Secure communications of chaotic systems with robust performance via fuzzy observer-based design. IEEE Trans. Fuzzy Syst. 9(1), 212–220 (2001)
Yoneyama, J., Nishikawa, M., Katayama, H., Ichikawa, A.: Design of output feedback controllers for Takagi-Sugeno fuzzy systems. Fuzzy Sets Syst. 121(1), 127–148 (2001)
Tseng, C.S., Chen, B.S., Uang, H.J.: Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model. IEEE Trans. Fuzzy Syst. 9(3), 381–392 (2001)
Tong, S., Li, H.H.: Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets Syst. 131(2), 165–184 (2002)
Lo, J.C., Lin, M.L.: Observer-based robust H\(_\infty \) control for fuzzy systems using two-step procedure. IEEE Trans. Fuzzy Syst. 12(3), 350–359 (2004)
Lin, C., Wang, Q.G., Lee, T.H.: Improvement on observer-based H\(_\infty \) control for TS fuzzy systems. Automatica 41(9), 1651–1656 (2005)
Tseng, C.S., Hwang, C.K.: Fuzzy observer-based fuzzy control design for nonlinear systems with persistent bounded disturbances. Fuzzy Sets Syst. 158(2), 164–179 (2007)
Ting, C.S.: An observer-based approach to controlling time-delay chaotic systems via Takagi-Sugeno fuzzy model. Inf. Sci. 177(20), 4314–4328 (2007)
Besheer, A.H., Emara, H.M., Aziz, M.M.A.: Fuzzy based output-feedback H\(_\infty \) control for uncertain nonlinear systems: an LMI approach. IET Control Theory Appl. 1(4), 1176–1185 (2007)
Choi, H.H.: LMI-based nonlinear fuzzy observer-controller design for uncertain MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 15(5), 956–971 (2007)
Gao, Z., Shi, X., Ding, S.X.: Fuzzy state/disturbance observer design for T-S fuzzy systems with application to sensor fault estimation. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(3), 875 (2008)
Tseng, C.S.: A novel approach to H\(_\infty \) decentralized fuzzy observer-based fuzzy control design for nonlinear interconnected systems. IEEE Trans. Fuzzy Syst. 16(5), 1337–1350 (2008)
Lin, C., Wang, Q.G., Lee, T., He, Y.: Design of observer-based control for fuzzy time-delay systems. IEEE Trans. Fuzzy Syst. 16(2), 534–543 (2008)
Chen, B., Liu, X.P., Tong, S.C., Lin, C.: Observer-based stabilization of T-S fuzzy systems with input delay. IEEE Trans. Fuzzy Syst. 16(3), 652–663 (2008)
Guerra, T.M., Kruszewski, A., Vermeiren, L., Tirmant, H.: Conditions of output stabilization for nonlinear models in the Takagi-Sugeno’s form. Fuzzy Sets Syst. 157(9), 1248–1259 (2006)
Lendek, Z., Lauber, J., Guerra, T.M., Babuška, R., De Schutter, B.: Adaptive observers for T-S fuzzy systems with unknown polynomial inputs. Fuzzy Sets Syst. 161(15), 2043–2065 (2010)
Lendek, Z., Babuska, R., De Schutter, B.: Sequential stability analysis and observer design for distributed TS fuzzy systems. Fuzzy Sets Syst. 174(1), 1–30 (2011)
Tanaka, K., Ohtake, H., Seo, T., Tanaka, M., Wang, H.O.: Polynomial fuzzy observer designs: a sum-of-squares approach. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 42(5), 1330–1342 (2012)
Liu, Y.J., Tong, S., Chen, C.L.P.: Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics. IEEE Trans. Fuzzy Syst. 21(2), 275–288 (2013)
Lam, H.K., Li, H., Liu, H.: Stability analysis and control synthesis for fuzzy observer-based controller of nonlinear systems: a fuzzy model-based control approach. IET Control Theory Appl. 7(5), 663–672 (2013)
Chadli, M., Karimi, H.R.: Robust observer design for unknown inputs Takagi-Sugeno models. IEEE Trans. Fuzzy Syst. 21(1), 158–164 (2013)
Li, J., Li, J., Xia, Z.: Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear systems. Int. J. Uncertain. Fuzziness. Knowl.-Based Syst. 21(03), 435–454 (2013)
Han, H., Higaki, Y., Lam, H.K.: Fuzzy disturbance observer for a class of polynomial fuzzy control systems. In: Proceedings of the 2014 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2014), pp. 2306–2312. IEEE (2014)
Wen, S., Zeng, Z., Huang, T.: Observer-based H\(_\infty \) fuzzy control for discrete-time Takagi-Sugeno fuzzy mixed delay systems with random packet losses and multiplicative noises. Int. J. Syst. Sci. 46(1), 159–169 (2015)
Moodi, H., Farrokhi, M.: Robust observer-based controller design for Takagi-Sugeno systems with nonlinear consequent parts. Fuzzy Sets Syst. 273, 141–154 (2015)
Liu, C., Lam, H.K.: Design of polynomial fuzzy observer-controller with sampled-output measurements for nonlinear systems considering unmeasurable premise variables. IEEE Trans. Fuzzy Syst. (2015, Accepted to appear)
Lam, H.K., Leung, F.H.F., Tam, P.K.S.: A switching controller for uncertain nonlinear systems. IEEE Control Syst. Mag. 22(1), 7–14 (2002)
Lam, H.K., Leung, F.H.F., Lee, Y.S.: Design of a switching controller for nonlinear systems with unknown parameters based on a fuzzy logic approach. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34(2), 1068–1074 (2004)
Lam, H.K., Leung, F.H.F.: Synchronization of uncertain chaotic systems based on the fuzzy model-based approach. Int. J. Bifurc. Chaos 16(5), 1435–1444 (2006)
Lam, H.K., Leung, F.H.F.: Fuzzy combination of linear state-feedback and switching controllers. Electron. Lett. 40(7), 410 (2004)
Lam, H.K., Leung, F.H.F.: Fuzzy combination of fuzzy and switching state-feedback controllers for nonlinear systems subject to parameter uncertainties. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 35(2), 269–281 (2005)
Lam, H.K., Leung, F.H.F.: Fuzzy rule-based combination of linear and switching state-feedback controllers. Fuzzy Sets Syst. 156(2), 153–184 (2005)
Xiu, Z., Ren, G.: Stability analysis and systematic design of Takagi-Sugeno fuzzy control systems. Fuzzy Sets Syst. 151(1), 119–138 (2005)
Dong, J., Yang, G.H.: State feedback control of continuous-time T-S fuzzy systems via switched fuzzy controllers. Inf. Sci. 178(6), 1680–1695 (2008)
Dong, J., Yang, G.H.: Dynamic output feedback control synthesis for continuous-time T-S fuzzy systems via a switched fuzzy control scheme. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(4), 1166–1175 (2008)
Chang, W., Park, J.B., Joo, Y.H., Chen, G.: Design of robust fuzzy model-based controller with sliding mode control for SISO nonlinear systems. Fuzzy Sets Syst. 125(1), 1–22 (2002)
Ho, D.W.C., Niu, Y.: Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control. IEEE Trans. Fuzzy Syst. 15(3), 350–358 (2007)
Lam, H.K.: Design of stable fuzzy controller for non-linear systems subject to imperfect premise matching based on grid-point approach. IET Control Theory Appl. 4(12), 2770–2780 (2010)
Li, H., Yu, J., Hilton, C., Liu, H.: Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach. IEEE Trans. Ind. Electron. 60(8), 3328–3338 (2013)
Lam, H.K., Narimani, M., Li, H., Liu, H.: Stability analysis of polynomial-fuzzy model-based control systems using switching polynomial Lyapunov function. IEEE Trans. Fuzzy Syst. 21(5), 800–813 (2013)
Liang, Y.W., Chen, C.C., Xu, S.S.D.: Study of reliable design using T-S fuzzy modeling and integral sliding mode control schemes. Int. J. Fuzzy Syst. 15(2), 233–243 (2013)
Han, H., Lam, H.K.: Discrete sliding-mode control for a class of T-S fuzzy models with modeling error. J. Adv. Comput. Intell. Intell. Inf. 18(6), 908–917 (2014)
Ngo, Q.H., Nguyen, N.P., Nguyen, C.N., Tran, T.H., Hong, K.S.: Fuzzy sliding mode control of container cranes. Int. J. Control Autom. Syst. 13(2), 1–7 (2015)
Wang, T., Tong, S.: H\(_\infty \) control design for discrete-time switched fuzzy systems. Neurocomputing 151, 782–789 (2015)
Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)
Katayama, H., Ichikawa, A.: H\(_\infty \) control for sampled-data nonlinear systems described by Takagi-Sugeno fuzzy systems. Fuzzy Sets Syst. 148(3), 431–452 (2004)
Yoneyama, J., Nishikawa, M., Katayama, H., Ichikawa, A.: Output stabilization of Takagi-Sugeno fuzzy systems. Fuzzy Sets Syst. 111(2), 253–266 (2000)
Lam, H.K., Leung, F.H.F.: Design and stabilization of sampled-data neural-network-based control systems. IEEE Trans. Syst. Man, Cybern. Part B 36(5), 995–1005 (2006)
Lam, H.K., Leung, F.H.F.: Sampled-data fuzzy controller for time-delay nonlinear system: LMI-based and fuzzy model-based approaches. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 37(3), 617–629 (2007)
Lam, H.K., Ling, W.K.: Sampled-data fuzzy controller for continuous nonlinear systems. IET Control Theory Appl. 2(1), 32–39 (2008)
Lam, H.K., Seneviratne, L.D.: Tracking control of sampled-data fuzzy model-based control systems. IET Control Theory Appl. 3(1), 56–67 (2009)
Lam, H.K.: Sampled-data fuzzy model-based control systems: stability analysis with consideration of analogue-to-digital converter and digital-to-analogue converter. Control Theory Appl., IET 4(7), 1131–1144 (2010)
Lien, C.H., Yu, K.W., Huang, C.T., Chou, P.Y., Chung, L.Y., Chen, J.D.: Robust H\(_\infty \) control for uncertain T-S fuzzy time-delay systems with sampled-data input and nonlinear perturbations. Nonlinear Anal.: Hybrid Syst. 4(3), 550–556 (2010)
Lee, H.J., Tomizuka, M.: Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach. IEEE Trans. Fuzzy Syst. 18(2), 251–260 (2010)
Wu, Z.G., Shi, P., Su, H., Chu, J.: Sampled-data fuzzy control of chaotic systems based on a T-S fuzzy model. IEEE Trans. Fuzzy Syst. 22(1), 153–163 (2014)
Li, H., Jing, X., Lam, H.K., Shi, P.: Fuzzy sampled-data control for uncertain vehicle suspension systems. IEEE Trans. Fuzzy Syst. 44(7), 1111–1126 (2014)
Koo, G.B., Park, J.B., Joo, Y.H.: LMI condition for sampled-data fuzzy control of nonlinear systems. Electron. Lett. 51(1), 29–31 (2014)
Wang, Z.P., Wu, H.N.: On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach. IEEE Trans. Cybern. 45(4), 819–829 (2015)
Jiang, X.: On sampled-data fuzzy control design approach for T-S model-based fuzzy systems by using discretization approach. Inf. Sci. 296, 307–314 (2015)
Gao, H., Chen, T.: Stabilization of nonlinear systems under variable sampling: a fuzzy control approach. IEEE Trans. Fuzzy Syst. 15(5), 972–983 (2007)
Yang, D., Cai, K.Y.: Reliable H\(_\infty \) nonuniform sampling fuzzy control for nonlinear systems with time delay. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(6), 1606–1613 (2008)
Zhu, X.L., Chen, B., Yue, D., Wang, Y.: An improved input delay approach to stabilization of fuzzy systems under variable sampling. IEEE Trans. Fuzzy Syst. 20(2), 330–341 (2012)
Yang, F., Zhang, H., Wang, Y.: An enhanced input-delay approach to sampled-data stabilization of T-S fuzzy systems via mixed convex combination. Nonlinear Dyn. 75(3), 501–512 (2014)
Shang, Z., Zhu, X.L.: Improved H\(_\infty \) stabilization criterion for nonuniform sampling fuzzy systems. Int. J. Appl. Math. Stat. 52(1), 41–51 (2014)
Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146–155 (1993)
Wang, L.X.: Adaptive Fuzzy Systems and Control - Design and Stability Analysis. Prentice Hall, Englewood Cliffs (1994)
Chen, B.S., Lee, C.H., Chang, Y.C.: H\(_\infty \) tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach. IEEE Trans. Fuzzy Syst. 4(1), 32–43 (1996)
Chai, T., Tong, S.: Fuzzy direct adaptive control for a class of nonlinear systems. Fuzzy Sets Syst. 103(3), 379–387 (1999)
Tsay, D.L., Chung, H.Y., Lee, C.J.: The adaptive control of nonlinear systems using the Sugeno-type of fuzzy logic. IEEE Trans. Fuzzy Syst. 7(2), 225–229 (1999)
Yu, W.S., Sun, C.J.: Fuzzy model based adaptive control for a class of nonlinear systems. IEEE Trans. Fuzzy Syst. 9(3), 413–425 (2001)
Tong, S., Li, H.X.: Direct adaptive fuzzy output tracking control of nonlinear systems. Fuzzy Sets Syst. 128(1), 107–115 (2002)
Li, H.X., Tong, S.: A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans. Fuzzy Syst. 11(1), 24–34 (2003)
Essounbouli, N., Hamzaoui, A.: Direct and indirect robust adaptive fuzzy controllers for a class of nonlinear systems. Int. J. Control Autom. Syst. 4(2), 146 (2006)
Lian, K.Y., Tu, H.W., Liou, J.J.: Stability conditions for LMI-based fuzzy control from viewpoint of membership functions. IEEE Trans. Fuzzy Syst. 14(6), 874–884 (2006)
Wang, M., Chen, B., Dai, S.L.: Direct adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear systems. Fuzzy Sets Syst. 158(24), 2655–2670 (2007)
Kim, J.H., Hyun, E., Park, M.: Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model. IEEE Trans. Fuzzy Syst. 15(3), 359–369 (2007)
Labiod, S., Guerra, T.M.: Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems. Fuzzy Sets Syst. 158(10), 1126–1137 (2007)
Wai, R.J., Kuo, M.A., Lee, J.D.: Cascade direct adaptive fuzzy control design for a nonlinear two-axis inverted-pendulum servomechanism. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(2), 439–454 (2008)
Phan, P.A., Gale, T.J.: Direct adaptive fuzzy control with a self-structuring algorithm. Fuzzy Sets Syst. 159(8), 871–899 (2008)
Chen, B., Liu, X., Liu, K., Lin, C.: Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6), 1530–1535 (2009)
Hsueh, Y.C., Su, S.F., Tao, C.W., Hsiao, C.C.: Robust L\(_2\)-gain compensative control for direct-adaptive fuzzy control-system design. IEEE Trans. Fuzzy Syst. 18(4), 661–673 (2010)
Liu, Y.J., Tong, S.: Adaptive fuzzy control for a class of unknown nonlinear dynamical systems. Fuzzy Sets Syst. 263, 49–70 (2015)
Wang, J., Rad, A.B., Chan, P.T.: Indirect adaptive fuzzy sliding mode control: Part I: fuzzy switching. Fuzzy Sets Syst. 122(1), 21–30 (2001)
Park, C.W., Cho, Y.W.: Adaptive tracking control of flexible joint manipulator based on fuzzy model reference approach. IEE Proc.-Control Theory Appl. 150(2), 198–204 (2003)
Blažič, S., Škrjanc, I., Matko, D.: Globally stable direct fuzzy model reference adaptive control. Fuzzy Sets Syst. 139(1), 3–33 (2003)
Park, C.W., Park, M.: Adaptive parameter estimator based on TS fuzzy models and its applications to indirect adaptive fuzzy control design. Inf. Sci. 159(1–2), 125–139 (2004)
Park, C.W., Cho, Y.W.: TS model based indirect adaptive fuzzy control using online parameter estimation. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34(6), 2293–2302 (2004)
Kung, C.C., Chen, T.H.: Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems. Fuzzy Sets Syst. 155(2), 292–308 (2005)
Zhang, K., Jiang, B., Staroswiecki, M.: Dynamic output feedback-fault tolerant controller design for Takagi-Sugeno fuzzy systems with actuator faults. IEEE Trans. Fuzzy Syst. 18(1), 194–201 (2010)
Han, C., Wu, L., Lam, H.K., Zeng, Q.: Nonfragile control with guaranteed cost of T-S fuzzy singular systems based on parallel distributed compensation. IEEE Trans. Fuzzy Syst. 22(5), 1183–1196 (2014)
Qiu, J., Feng, G., Gao, H.: Fuzzy model-based piecewise static-output-feedback controller design for networked nonlinear systems. IEEE Trans. Fuzzy Syst. 18(5), 919–934 (2010)
Qiu, J., Feng, G., Gao, H.: Asynchronous output-feedback control of networked nonlinear systems with multiple packet dropouts: T-S fuzzy affine model-based approach. IEEE Trans. Fuzzy Syst. 19(6), 1014–1030 (2011)
Yang, F., Zhang, H.: T-S model-based relaxed reliable stabilization of networked control systems with time-varying delays under variable sampling. Int. J. Fuzzy Syst. 13(4), 260–269 (2011)
Peng, C., Han, Q.L., Yue, D.: To transmit or not to transmit: a discrete event-triggered communication scheme for networked Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 21(1), 164–170 (2013)
Wu, L., Ho, D.W.C.: Fuzzy filter design for Itô stochastic systems with application to sensor fault detection. IEEE Trans. Fuzzy Syst. 17(1), 233–242 (2009)
Liu, M., Cao, X., Shi, P.: Fuzzy model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults. IEEE Trans. Fuzzy Syst. 21(5), 789–799 (2013)
Liu, M., Cao, X., Shi, P.: Fault estimation and tolerant control for fuzzy stochastic systems. IEEE Trans. Fuzzy Syst. 21(2), 221–229 (2013)
Sheng, L., Gao, M., Zhang, W.: Dissipative control for Markov jump non-linear stochastic systems based on T-S fuzzy model. Int. J. Syst. Sci. 45(5), 1213–1224 (2014)
Benzaouia, A., Hmamed, A., Hajjaji, E.L.: A., : Stabilization of controlled positive discrete-time T-S fuzzy systems by state feedback control. Int. J. Adapt. Control. Signal Process. 24(12), 1091–1106 (2010)
Mao, Y., Zhang, H., Dang, C.: Stability analysis and constrained control of a class of fuzzy positive systems with delays using linear copositive Lyapunov functional. Circuits Syst. Signal Process. 31(5), 1863–1875 (2012)
Wu, Y., Luo, H., Zhang, H.: Stability analysis of discrete-time fuzzy positive systems with time delays. J. Intell. Fuzzy Syst. 25(4), 893–905 (2013)
Mao, Y., Zhang, H., Qin, Y., Dang, C.: Stability and constrained control of a class of discrete-time fuzzy positive systems with time-varying delays. Circuits Syst. Signal Process. 32(2), 889–904 (2013)
Benzaouia, A., Mesquine, F., Benhayoun, M., Schulte, H., Georg, S.: Stabilization of positive constrained T-S fuzzy systems: application to a buck converter. J. Frankl. Inst. 351(8), 4111–4123 (2014)
Fadali, M.S., Jafarzadeh, S.: Stability analysis of positive interval type-2 TSK systems with application to energy markets. IEEE Trans. Fuzzy Syst. 22(4), 1031–1038 (2014)
Roubos, J.A., Mollov, S., Babuška, R., Verbruggen, H.B.: Fuzzy model-based predictive control using Takagi-Sugeno models. Int. J. Approx. Reason. 22(1), 3–30 (1999)
Espinosa, J.J., Vandewalle, J.: Predictive control using fuzzy models. Advances in Soft Computing, pp. 187–200. Springer, New York (1999)
Huang, Y.L., Lou, H.H., Gong, J.P., Edgar, T.F.: Fuzzy model predictive control. IEEE Trans. Fuzzy Syst. 8(6), 665–678 (2000)
Mollov, S., Babuska, R., Abonyi, J., Verbruggen, H.B.: Effective optimization for fuzzy model predictive control. IEEE Trans. Fuzzy Syst. 12(5), 661–675 (2004)
Li, N., Li, S.Y., Xi, Y.G.: Multi-model predictive control based on the Takagi-Sugeno fuzzy models: a case study. Inf. Sci. 165(3), 247–263 (2004)
Mazinan, A.H., Sadati, N.: Multiple modeling and fuzzy predictive control of a tubular heat exchanger system. WSEAS Trans. Syst. Control 3(4), 249–258 (2008)
Xia, Y., Yang, H., Shi, P., Fu, M.: Constrained infinite-horizon model predictive control for fuzzy discrete-time systems. IEEE Trans. Fuzzy Syst. 18(2), 429–436 (2010)
Wang, B., Zhang, J., Zhu, D., Chen, D.: Takagi-Sugeno fuzzy predictive control for a class of nonlinear system with constrains and disturbances. J. Comput. Nonlinear Dyn. 10(5), 054505 (2015)
Wang, Y.W., Guan, Z.H., Wang, H.O.: Impulsive synchronization for Takagi-Sugeno fuzzy model and its application to continuous chaotic system. Phys. Lett. A 339(3), 325–332 (2005)
Liu, X., Zhong, S.: T-S fuzzy model-based impulsive control of chaotic systems with exponential decay rate. Phys. Lett. A 370(3), 260–264 (2007)
Zhong, Q., Bao, J., Yu, Y., Liao, X.: Impulsive control for T-S fuzzy model-based chaotic systems. Math. Comput. Simul. 79(3), 409–415 (2008)
Jiang, H.B., Yu, J.J., Zhou, C.G.: Robust fuzzy control of nonlinear fuzzy impulsive systems with time-varying delay. IET Control Theory Appl. 2(8), 654–661 (2008)
Zheng, Y., Chen, G.: Fuzzy impulsive control of chaotic systems based on TS fuzzy model. Chaos Solitons Fractals 39(4), 2002–2011 (2009)
Liu, Y., Zhao, S., Lu, J.: A new fuzzy impulsive control of chaotic systems based on T-S fuzzy model. IEEE Trans. Fuzzy Syst. 19(2), 393–398 (2011)
Zhang, H., Yan, H., Liu, T., Chen, Q.: Fuzzy controller design for nonlinear impulsive fuzzy systems with time delay. IEEE Trans. Fuzzy Syst. 19(5), 844–856 (2011)
Khalil, H.K., Grizzle, J.W.: Nonlinear Syst. Prentice hall, Englewood Cliffs (1996)
Vidyasagar, M.: Nonlinear Systems Analysis. Society for Industrial Mathematics, Philadelphia (2002)
Zhang, H., Xie, X.: Relaxed stability conditions for continuous-time T-S fuzzy control systems via augmented multi-indexed matrix approach. IEEE Trans. Fuzzy Syst. 19(3), 478–492 (2011)
Ding, B.: Homogeneous polynomially nonquadratic stabilization of discrete-time Takagi-Sugeno systems via nonparallel distributed compensation law. IEEE Trans. Fuzzy Syst. 18(5), 994–1000 (2010)
Papachristodoulou, A., Prajna, S.: A tutorial on sum of squares techniques for system analysis. In: Proceedings of the American Control Conference (ASCC), pp. 2686–2700. Portland, OR, USA (2005)
Prajna, S., Papachristodoulou, A., Parrilo, P.A.: Nonlinear control synthesis by sum-of-squares optimization: a lyapunov-based approach. In: Proceedings of the Asian Control Conference (ASCC), vol. 1, pp. 157–165. Melbourne, Australia (2004)
Cao, K., Gao, X., Vasilakos, T., Pedrycz, W.: Analysis of stability and robust stability of polynomial fuzzy model-based control systems using a sum-of-squares approach. Soft. Comput. 18(3), 433–442 (2014)
Prajna, S., Papachristodoulou, A., Parrilo, P.A.: Introducing SOSTOOLS: a general purpose sum of squares programming solver. In: Proceedings of the 41st IEEE Conference on Decision and Control, vol. 1, pp. 741–746. Las Vegas, Nevada, USA (2002)
Prajna, S., Papachristodoulou, A., Parrilo, P.A.: SOSTOOLS - sum of squares optimization toolbox, user’s guide (2002)
Narimani, M., Lam, H.K.: SOS-based stability analysis of polynomial fuzzy model-based control systems via polynomial membership functions. IEEE Trans. Fuzzy Syst. 18(5), 862–871 (2010)
Liu, C., Lam, H.K., Zhang, X., Li, H., Ling, S.H.: Relaxed stability conditions based on Taylor series membership functions for polynomial fuzzy model-based control systems. In: Proceedings of the 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2014), pp. 2111–2118. IEEE (2014)
Lam, H.K., Wu, L., Zhao, Y.: Linear matrix inequalities-based membership function-dependent stability analysis for non-parallel distributed compensation fuzzy model-based control systems. IET Control Theory Appl. 8(8), 614–625 (2014)
Johansson, M., Rantzer, A., Arzen, K.E.: Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Syst. 7(6), 713–722 (1999)
Feng, M., Harris, C.J.: Piecewise Lyapunov stability conditions of fuzzy systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 31(2), 259–262 (2001)
Feng, G.: Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 11(5), 605–612 (2003)
Feng, G.: H\(_\infty \) controller design of fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 34(1), 283–292 (2004)
Feng, G., Chen, C.L., Sun, D., Zhu, Y.: H\(_\infty \) controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities. IEEE Trans. Fuzzy Syst. 13(1), 94–103 (2005)
Ohtake, H., Tanaka, K., Wang, H.O.: Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 36(1), 13–23 (2006)
Lendek, Z., Lauber, J., Guerra, T.M.: Periodic Lyapunov functions for periodic T-S systems. Syst. Control Lett. 62(4), 303–310 (2013)
Mao, Y., Zhang, H., Xu, S.: Exponential stability and asynchronous stabilization of a class of switched nonlinear system via T-S fuzzy model. IEEE Trans. Fuzzy Syst. 22(4), 817–828 (2014)
Tanaka, K., Hori, T., Wang, H.O.: A multiple Lyapunov function approach to stabilization of fuzzy control systems. IEEE Trans. Fuzzy Syst. 11(4), 582–589 (2003)
Guerra, T.M., Vermeiren, L.: LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno’s form. Automatica 40(5), 823–829 (2004)
Ding, B.C., Sun, H.X., Yang, P.: Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno’s form. Automatica 42(3), 503–508 (2006)
Rhee, B.J., Won, S.: A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design. Fuzzy Sets Syst. 157(9), 1211–1228 (2006)
Tanaka, K., Ohtake, H., Wang, H.O.: A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions. IEEE Trans. Fuzzy Syst. 15(3), 333–341 (2007)
Li, J., Zhou, S., Xu, S.: Fuzzy control system design via fuzzy Lyapunov functions. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(6), 1657–1661 (2008)
Bernal, M., Guerra, T.M.: Generalized nonquadratic stability of continuous-time Takagi-Sugeno models. IEEE Trans. Fuzzy Syst. 18(4), 815–822 (2010)
Mozelli, L.A., Palhares, R.M., Avellar, G.S.C.: A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems. Inf. Sci. 179(8), 1149–1162 (2009)
Chang, X.H., Yang, G.H.: Relaxed stabilization conditions for continuous-time Takagi-Sugeno fuzzy control systems. Inf. Sci. 180(17), 3273–3287 (2010)
Mozelli, L.A., Palhares, R.M., Mendes, E.M.A.M.: Equivalent techniques, extra comparisons and less conservative control design for Takagi-Sugeno (T-S) fuzzy systems. IET Control Theory Appl. 4(12), 2813–2822 (2010)
Lee, D.H., Park, J.B., Joo, Y.H.: Improvement on nonquadratic stabilization of discrete-time Takagi-Sugeno fuzzy systems: multiple-parameterization approach. IEEE Trans. Fuzzy Syst. 18(2), 425–429 (2010)
Lam, H.K., Seneviratne, L.D., Ban, X.: Fuzzy control of non-linear systems using parameter-dependent polynomial fuzzy model. IET Control Theory Appl. 6(11), 1645–1653 (2012)
Lam, H.K., Lauber, J.: Membership-function-dependent stability analysis of fuzzy model-based control systems using fuzzy Lyapunov functions. Inf. Sci. 232, 253–266 (2013)
Xie, X., Ma, H., Zhao, Y., Ding, D.W., Wang, Y.: Control synthesis of discrete-time T-S fuzzy systems based on a novel non-PDC control scheme. IEEE Trans. Fuzzy Syst. 21(1), 147–157 (2013)
Faria, F.A., Silva, G.N., Oliveira, V.A.: Reducing the conservatism of LMI-based stabilisation conditions for T-S fuzzy systems using fuzzy Lyapunov functions. Int. J. Syst. Sci. 44(10), 1956–1969 (2013)
Campos, V.C.S., Souza, F.O., Tôrres, L.A.B., Palhares, R.M.: New stability conditions based on piecewise fuzzy Lyapunov functions and tensor product transformations. IEEE Trans. Fuzzy Syst. 21(4), 748–760 (2013)
Duong, C.C., Guelton, K., Manamanni, N.: A SOS based alternative to LMI approaches for non-quadratic stabilization of continuous-time Takagi-Sugeno fuzzy systems. In: Proceedings of the 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2013), pp. 1–7. IEEE (2013)
Kim, S.H.: Relaxation technique for a T-S fuzzy control design based on a continuous-time fuzzy weighting-dependent Lyapunov function. IEEE Trans. Fuzzy Syst. 21(4), 761–766 (2013)
Zhang, B.: Stability control of flexible joint robot based T-S fuzzy model using fuzzy Lyapunov function. J. Converg. Inf. Technol. 8(1) (2013)
Cao, K., Gao, X.Z., Lam, H.K., Vasilakos, A.V., Pedrycz, W.: A new relaxed stability condition for Takagi-Sugeno fuzzy control systems using quadratic fuzzy Lyapunov functions and staircase membership functions. Int. J. Fuzzy Syst. 16(3), 327 (2014)
Lee, D.H., Joo, Y.H., Tak, M.H.: Local stability analysis of continuous-time Takagi-Sugeno fuzzy systems: A fuzzy Lyapunov function approach. Inf. Sci. 257, 163–175 (2014)
Chang, W.J., Chang, Y.C., Ku, C.C.: Passive fuzzy control via fuzzy integral Lyapunov function for nonlinear ship drum-boiler systems. J. Dyn. Syst. Meas. Control 137(4), 041008 (2015)
Tognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D.: H\(_2\) and H\(_\infty \) nonquadratic stabilisation of discrete-time Takagi-Sugeno systems based on multi-instant fuzzy Lyapunov functions. Int. J. Syst. Sci. 46(1), 76–87 (2015)
Zhao, X., Zhang, L., Shi, P., Karimi, H.: Novel stability criteria for T-S fuzzy systems. IEEE Trans. Fuzzy Syst. 22(2), 425–429 (2013)
Sala, A., Ariño, C.: Relaxed stability and performance conditions for Takagi-Sugeno fuzzy systems with knowledge on membership function overlap. IEEE Trans. Syst. Man Cybern. Part : Cybern. 37(3), 727–732 (2007)
Sala, A., Ariño, C.: Relaxed stability and performance LMI conditions for Takagi-Sugeno fuzzy systems with polynomial constraints on membership function shapes. IEEE Trans. Fuzzy Syst. 16(5), 1328–1336 (2008)
Lam, H., Lauber, J.: Stability analysis of nonlinear-function fuzzy model-based control systems. J. Frankl. Inst. 349(10), 3102–3120 (2012)
Lam, H.K., Tsai, S.H.: Stability analysis of polynomial-fuzzy model-based control systems with mismatched premise membership functions. IEEE Trans. Fuzzy Syst. 22(1), 223–229 (2014)
Lam, H.K., Liu, C., Wu, L., Zhao, X.: Polynomial fuzzy model-based control systems: Stability analysis via approximated membership functions considering sector nonlinearity of control input. IEEE Trans. Fuzzy Syst. (2015, Accepted to appear)
Boyd, S.P.: Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1994)
El Ghaoui, L., Niculescu, S.I.: Advances in linear matrix inequality methods in control. Society for Industrial Mathematics (2000)
Narimani, M., Lam, H.K.: Relaxed LMI-based stability conditions for Takagi-Sugeno fuzzy control systems using regional-membership-function-shape-dependent analysis approach. IEEE Trans. Fuzzy Syst. 17(5), 1221–1228 (2009)
Kruszewski, A., Sala, A., Guerra, T., Arino, C.: A triangulation approach to asymptotically exact conditions for fuzzy summations. IEEE Trans. Fuzzy Syst. 17(5), 985–994 (2009)
Narimani, M., Lam, H.K., Dilmaghani, R., Wolfe, C.: LMI-based stability analysis of fuzzy model-based control systems using approximated polynomial membership functions. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 41(3), 713–724 (2011)
Zhao, Y., Xiao, B., Liu, C., Li, H., Lam, H.K.: Relaxed LMI-based stability conditions for fuzzy model-based control systems under imperfect premise matching: Approximated membership function approach. In: Proceedings of the 2014 11th World Congress on Intelligent Control and Automation (WCICA 2014), pp. 251–256. IEEE (2014)
Precup, R.E., Hellendoorn, H.: A survey on industrial applications of fuzzy control. Comput. Ind. 62(3), 213–226 (2011)
Rao, M.V.C., Prahlad, V.: A tunable fuzzy logic controller for vehicle-active suspension systems. Fuzzy Sets Syst. 85(1), 11–21 (1997)
Cao, J., Liu, H., Li, P., Brown, D.: An interval type-2 fuzzy logic controller for quarter-vehicle active suspensions. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. 222(8), 1361 (2008)
Cao, J., Li, P., Liu, H.: An interval fuzzy controller for vehicle active suspension systems. IEEE Trans. Intell. Transp. Syst. 11(4), 885–895 (2010)
Su, X., Yang, X., Shi, P., Wu, L.: Fuzzy control of nonlinear electromagnetic suspension systems. Mechatronics 24(4), 328–335 (2014)
Malki, H.A., Misir, D., Feigenspan, D., Chen, G.: Fuzzy pid control of a flexible-joint robot arm with uncertainties from time-varying loads. IEEE Trans. Control Syst. Technol. 5(3), 371–378 (1997)
Chang, W.J., Shih, Y.J.: Fuzzy control of multiplicative noised nonlinear systems subject to actuator saturation and H\(_\infty \) performance constraints. Neurocomputing 148, 512–520 (2015)
Chiu, C.S., Chiang, T.S.: Robust output regulation of T-S fuzzy systems with multiple time-varying state and input delays. IEEE Trans. Fuzzy Syst. 17(4), 962–975 (2009)
So, W.C., Tse, C.K., Lee, Y.S.: Development of a fuzzy logic controller for DC/DC converters: design, computer simulation, and experimental evaluation. IEEE Trans. Power Electron. 11(1), 24–32 (1996)
Leung, F.H.F., Wong, L.K., Tam, P.K.S., Lam, H.K.: Realization of analog fuzzy logic control for PWM boost converters. J. Circuits Syst. Comput. 8(3), 411–419 (1998)
Lin, P.Z., Lin, C.M., Hsu, C.F., Lee, T.T.: Type-2 fuzzy controller design using a sliding-mode approach for application to DC-DC converters. IEE Proc.-Electr. Power Appl. 152(6), 1482–1488 (2005)
Lian, K.Y., Liou, J.J., Huang, C.Y.: LMI-based integral fuzzy control of DC-DC converters. IEEE Trans. Fuzzy Syst. 14(1), 71–80 (2006)
Leung, F.H.F., Lam, H.K., Tam, P.K.S.: Fuzzy control of DC-DC switching converters: stability and robustness analysis. Aust. J. Electr. Electron. Eng. 4(1), 91–99 (2008)
Lam, H.K., Tan, S.C.: Stability analysis of fuzzy model-based control systems: application on regulation of switching DC-DC converter. IET Control Theory Appl. 3(8), 1093–1106 (2009)
Elmas, C., Deperlioglu, O., Sayan, H.H.: Adaptive fuzzy logic controller for DC-DC converters. Expert Syst. Appl. 36(2), 1540–1548 (2009)
Lian, K.Y., Hong, C.W.: Current-sensorless flyback converters using integral T-S fuzzy approach. Int. J. Fuzzy Syst. 15(1), 66–74 (2013)
Vu, N.T.T., Yu, D.Y., Choi, H.H., Jung, J.W.: T-S fuzzy-model-based sliding-mode control for surface-mounted permanent-magnet synchronous motors considering uncertainties. IEEE Trans. Ind. Electron. 60(10), 4281–4291 (2013)
Wang, M., Chen, B., Liu, X., Shi, P.: Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets Syst. 159(8), 949–967 (2008)
Vembarasan, V., Balasubramaniam, P.: Chaotic synchronization of Rikitake system based on T-S fuzzy control techniques. Nonlinear Dyn. 74(1–2), 31–44 (2013)
Lee, T.H., Lam, H.K., Leung, F.H.F., Tam, P.K.S.: A practical fuzzy logic controller for the path tracking of wheeled mobile robots. IEEE Control Syst. Mag. 23(2), 60–65 (2003)
Ordónez, R., Passino, K.M.: Stable multi-input multi-output adaptive fuzzy/neural control. IEEE Trans. Fuzzy Syst. 7(3), 345–353 (1999)
Leung, F.H.F., Lam, H.K., Ling, S.H., Tam, P.K.S.: Optimal and stable fuzzy controllers for nonlinear systems based on an improved genetic algorithm. IEEE Trans. Ind. Electron. 51(1), 172–182 (2004)
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Lam, HK. (2016). Introduction. In: Polynomial Fuzzy Model-Based Control Systems. Studies in Systems, Decision and Control, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-319-34094-4_1
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DOI: https://doi.org/10.1007/978-3-319-34094-4_1
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