Abstract
This paper is concerned with stabilization for a class of Takagi-Sugeno fuzzy neural networks (TSFNNs) with time-varying delays. An impulsive control scheme is employed to stabilize a TSFNN. We firstly establish the model of TSFNNs by using fuzzy sets and fuzzy reasoning and propose the problem of impulsive stabilization for this model. Then, we present several stabilization conditions based on Lyapunov function, inequality techniques and linear matrix inequality approach. Two numerical examples are provided to illustrate the efficiency of impulsive stabilization for TSFNNs by using fixed impulsive interval and variable impulsive intervals, respectively.
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Barazane L., Krishan M.M., Khwaldeh A.: An approach to the fuzzy variable structure control of induction motors. Arab. J. Sci. Eng. 33(2B), 453–472 (2008)
Cao Y.Y., Frank P.M.: Robust H ∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Trans. Fuzzy Syst. 8(4), 406–415 (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)
Cheng C.J.: Robust control of a class of neural networks with bounded uncertainties and time-varying delays. Comp. Appl. Math. 56(5), 1245–1254 (2008)
Cheng C.J.: Decentralized feedback control of uncertain cellular neural networks subject to time-varying delays and dead-zone input. Math. Comp. Model. 49(1–2), 386–392 (2009)
Guan Z.H., Qian T.H., Yu X.H.: On controllability and observability for a class of impulsive systems. Syst. Control Lett. 47(3), 247–257 (2002)
Gilli M.: Strange attractors in delayed cellular neural networks. IEEE Trans. Circuits Syst. 40(10), 849–853 (1993)
Jankowski S., Londei A., Lozowski A., Mazur C.: Synchronization and control in a cellular neural network of chaotic units by local pinnings. Int. J. Circuit Theory Appl. 24(3), 275–281 (1996)
Ho D.W.C., Niu Y.G.: Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control. IEEE Trans. Fuzzy Syst. 15(3), 350–358 (2007a)
Ho D.W.C., Sun J.T.: Stability of Takagi-Sugeno fuzzy delay systems with impulse. IEEE Trans. Fuzzy Syst. 15(5), 784–790 (2007b)
Hou Y.Y., Liao T.L., Yan J.J.: Stability analysis of Takagi-Sugeno fuzzy cellular neural networks with time-varying delays. IEEE Trans. Syst. Man Cybern. Part B 37(3), 720–726 (2007c)
Huang, L.: Linear Algebra in System and Control Theory, p. 211. Science Press, Beijing (1984)
Huang H., Ho D.W.C., Lam J.: Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Trans. Circuits Syst. II Express Briefs 52(5), 251–255 (2005)
Lakshmikantham V., Bainov D., Simeonov P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
Lee H.J., Park J.B., Chen G.: Robust fuzzy control of nonlinear systems with parametric uncertainties. IEEE Trans. Fuzzy Syst. 9(3), 369–379 (2001)
Liu X.Z., Wang Q.: Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays. IEEE Trans. Neural Netw. 19(1), 71–79 (2008)
Lou X.Y., Cui B.T.: Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays. Fuzzy Sets Syst. 158(24), 2746–2756 (2007)
Lu H.T.: Chaotic attractors in delayed neural networks. Phys. Lett. A 298(2–3), 109–116 (2002)
Rakkiyappan R., Balasubramaniam P., Cao J.D.: Global exponential stability results for neutral-type impulsive neural networks. Nonlinear Anal. Real World Appl. 11(1), 122–130 (2010)
Salim L., Seghir B.M.: Indirect fuzzy adaptive control of a class of SISO nonlinear systems. Arab. J. Sci. Eng. 31(1B), 61–74 (2006)
Samidurai R., Marshal Anthoni S., Balachandran K.: Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays. Nonlinear Anal. Hybrid Syst. 4(1), 103–112 (2010)
Sun J.T., Zhang Y.P.: Stability analysis of impulsive control systems. IEEE Proc. Control Theory Appl. 150(4), 331–334 (2003)
Tanaka K., Wang H.O.: Fuzzy Control Systems Design and Analysis. Wiley, New York (2001)
Takagi T., Sugeno M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC- 15(1), 116–132 (1985)
Xu S.Y., Chu Y.M., Lu J.W.: New results on global exponential stability of recurrent neural networks with time-varying delays. Phys. Lett. A 352(4–5), 371–379 (2006)
Xu S.Y., Lam J., Ho D.W.C.: A new LMI condition for delay-dependent asymptotic stability of delayed Hopfield neural networks. IEEE Trans. Circuits Syst. II Express Briefs 53(3), 230–234 (2006)
Yoneyama J.: Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays. Int. J. Inf. Sci. 178(8), 1935–1947 (2008)
Zhang H., Guan Z.H., Feng G.: Reliable dissipative control for stochastic impulsive systems. Automatica 44(4), 1004–1010 (2008)
Zhang X.M., Lu G.P., Zheng Y.F.: Stabilization of networked stochastic time-delay fuzzy systems with data dropout. IEEE Trans. Fuzzy Syst. 16(3), 798–807 (2008)
Zhang Q., Wei X., Xu. J.: Global asymptotic stability of Hopfield neural networks with transmission delays. Phys. Lett. A 318(4–5), 399–405 (2003)
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This work is partially supported by National Natural Science Foundation of China (No.61174021, No.61104155).
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Lou, X., Ye, Q. & Cui, B. Impulsive stabilization of fuzzy neural networks with time-varying delays. Arab. J. Math. 2, 65–79 (2013). https://doi.org/10.1007/s40065-012-0052-z
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DOI: https://doi.org/10.1007/s40065-012-0052-z