Advertisement

International Journal of Fuzzy Systems

, Volume 21, Issue 8, pp 2625–2631 | Cite as

Stability Analysis of T–S Fuzzy Control Systems Subject to Actuator Saturation

  • Zhenhuan WangEmail author
  • Yue Zhao
  • Hairui Du
  • Kairui Cao
Article
  • 14 Downloads

Abstract

In this paper, a stability analysis method based on a type of staircase membership functions is proposed for fuzzy control systems with actuator saturation. The staircase membership functions are used to approximate the membership functions of the fuzzy models. Due to the discreteness and finiteness of the values of staircase membership functions, the fuzzy summation inequalities describing the stability of closed-loop system can be converted to a finite number of linear matrix inequalities. The proposed method has a low degree of conservativeness since the information of membership functions is introduced into the stability analysis. Simulation results are given to show the effectiveness of the proposed methods.

Keywords

Fuzzy control systems Staircase membership functions Actuator saturation Attractive domains Linear matrix inequalities 

Notes

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (61640301, 61673130, and 61703120).

References

  1. 1.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 1, 116–132 (1985)CrossRefGoogle Scholar
  2. 2.
    Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, Hoboken (2004)Google Scholar
  3. 3.
    Liu, J., Wu, C., Wang, Z., Wu, L.: Reliable filter design for sensor networks using type-2 fuzzy framework. IEEE Trans. Ind. Inform. 13(4), 1742–1752 (2017)CrossRefGoogle Scholar
  4. 4.
    Tseng, C.-S., Chen, B.-S., Uang, H.-J.: Fuzzy tracking control design for nonlinear dynamic systems via TS fuzzy model. IEEE Trans. Fuzzy Syst. 9(3), 381–392 (2001)CrossRefGoogle Scholar
  5. 5.
    Liang, X., Zhang, J.-D., Li, W., Guo, B.-J., Wan, L., Xu, Y.-R.: TS fuzzy neural network control for autonomous underwater vehicles. Electr. Mach. Control 7, 018 (2010)Google Scholar
  6. 6.
    Yan, W.-X., Ji, Z.-C.: TS fuzzy model and control for three-phase shunt APF. Electr. Mach. Control 11, 017 (2010)MathSciNetGoogle Scholar
  7. 7.
    Zhang, L., Zhang, H., Gao, H.: Decentralized non-fragile event-triggered \({{H}_{\infty }}\) filtering for large-scaled power system based on TS fuzzy model. IEEE Access 6, 64540–64548 (2018)CrossRefGoogle Scholar
  8. 8.
    Chen, C., Liu, H., Guan, X.: \(H_{\infty }\) filtering of time-delay T-S fuzzy systems based on piecewise Lyapunov-Krasovskii functional. Signal Process. 89(10), 1998–2005 (2009)CrossRefGoogle Scholar
  9. 9.
    Chibani, A., Chadli, M., Shi, P., Braiek, N.B.: Fuzzy fault detection filter design for TS fuzzy systems in the finite-frequency domain. IEEE Trans. Fuzzy Syst. 25(5), 1051–1061 (2016)CrossRefGoogle Scholar
  10. 10.
    Wang, X.-S., Cheng, Y.-H., Yi, J.-Q.: A fuzzy actor-critic reinforcement learning network. Inf. Sci. 177(18), 3764–3781 (2007)CrossRefGoogle Scholar
  11. 11.
    Zhou, S., Lam, J., Zheng, W.X.: Control design for fuzzy systems based on relaxed nonquadratic stability and \(H_{\infty }\) performance conditions. IEEE Trans. Fuzzy Syst. 15(2), 188–199 (2007)CrossRefGoogle Scholar
  12. 12.
    Amaral, M.L., Martinez, P.R.: Less conservative fuzzy control for discrete-time Takagi-Sugeno systems. Math. Prob. Eng. 2011, 21 (2011)MathSciNetzbMATHGoogle Scholar
  13. 13.
    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)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yang, H., Li, X., Liu, Z., Zhao, L.: Robust fuzzy-scheduling control for nonlinear systems subject to actuator saturation via delta operator approach. Inf. Sci. 272, 158–172 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Chen, C.P., Ren, C.-E., Du, T.: Fuzzy observed-based adaptive consensus tracking control for second-order multiagent systems with heterogeneous nonlinear dynamics. IEEE Trans. Fuzzy Syst. 24(4), 906–915 (2016)CrossRefGoogle Scholar
  16. 16.
    Choi, H.D., Ahn, C.K., Shi, P., Wu, L., Lim, M.T.: Dynamic output-feedback dissipative control for TS fuzzy systems with time-varying input delay and output constraints. IEEE Trans. Fuzzy Syst. 25(3), 511–526 (2017)CrossRefGoogle Scholar
  17. 17.
    Zhang, D., Zhou, Z., Jia, X.: Networked fuzzy output feedback control for discrete-time Takagi-Sugeno fuzzy systems with sensor saturation and measurement noise. Inf. Sci. 457–458, 182–194 (2018)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Cao, Y.-Y., Lin, Z.: Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation. IEEE Trans. Fuzzy Syst. 11(1), 57–67 (2003)CrossRefGoogle Scholar
  19. 19.
    Ting, C.-S.: A robust fuzzy control approach to stabilization of nonlinear time-delay systems with saturating inputs. Int. J. Fuzzy Syst. 10(1), 50–60 (2008)MathSciNetGoogle Scholar
  20. 20.
    Zhao, Y., Gao, H.: Fuzzy-model-based control of an overhead crane with input delay and actuator saturation. IEEE Trans. Fuzzy Syst. 20(1), 181–186 (2012)CrossRefGoogle Scholar
  21. 21.
    Zhang, S.-T., Wang, S.-J.: Quadratic stable controller design of discrete fuzzy systems. Electr. Mach. Control 5, 020 (2008)Google Scholar
  22. 22.
    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)CrossRefGoogle Scholar
  23. 23.
    Lam, H.: Stability analysis of T-S fuzzy control systems using parameter-dependent Lyapunov function. IET Control Theor. Appl. 3(6), 750–762 (2009)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Springer Science & Business Media, Berlin (2001)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  • Zhenhuan Wang
    • 1
    Email author
  • Yue Zhao
    • 2
  • Hairui Du
    • 1
  • Kairui Cao
    • 1
  1. 1.Space Control and Inertial Technology Research CenterHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Control Science and EngineeringHarbin Institute of TechnologyHarbinChina

Personalised recommendations