Skip to main content
SpringerLink
Log in

Reliable control for nonlinear systems with stochastic actuators fault and random delays through a T-S fuzzy model approach

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

This paper considers the reliable control design for T-S fuzzy systems with probabilistic actuators faults and random time-varying delays. The faults of each actuator occurs randomly and its failure rates are governed by a set of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of each actuator and time-varying random delays, new fault model is proposed. Based on the new fuzzy model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of T-S fuzzy systems are derived by using Lyapunov functional method and linear matrix inequality (LMI) technique. It should be noted that the obtained criteria depend on not only the size of the delay, but also the probability distribution of it. Finally, a numerical example is given to show the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cao, Y., Frank, P. Analysis and synthesis of nonlinear time-delay systems via fuzzycontrol approach. IEEE Transactions on Fuzzy Systems, 8(2): 200–211 (2000)

    Article  Google Scholar 

  2. Cao, Y., Frank, P. Stability analysis and synthesis of nonlinear time-delay systems via linear T-S fuzzy models. Fuzzy Sets and Systems, 124(2): 213–229 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Guan, X., Chen, C. Delay-dependent guaranteed cost control for TSfuzzy systems with time delays. IEEE Transactions on Fuzzy Systems, 12(2): 236–249 (2004)

    Article  MATH  Google Scholar 

  4. Gao, Z., Breikin, T., Wang, H. Reliable observer-based control against sensor failures for systems with time delays in both state and input. IEEE Transactions on Systems, Man, and Cybernetics part A: Systems and Humans, 38(5): 1018–1029 (2008)

    Article  Google Scholar 

  5. He, X., Wang, Z., Zhou, D. Robust H∞ Filtering for Time-delay Systems With Probabilistic Sensor Faults. IEEE Signal Processing Letters, 16(5): 442–445 (2009)

    Article  Google Scholar 

  6. Liu, J., Gu, Z., Tian, E., Yan, R. New results on H∞ filter design for nonlinear systems with time-delay through a T-S fuzzy model approach. International Journal of Systems Science, 43(3): 426–442 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mao, X. Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Transactions on Automatic Control, 47(10): 1604–1612 (2002)

    Article  MathSciNet  Google Scholar 

  8. Peng, C., Tian, Y., Tian, E. Improved delay-dependent robust stabilization conditions of uncertain T–S fuzzy systems with time-varying delay. Fuzzy Sets and Systems, 159(20): 2713–2729 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Peng, C., Yue, D., Tian, Y. New approach on robust delay-dependent H∞ control for uncertain TSfuzzy systems with interval time-varying delay. IEEE Transactions on Fuzzy Systems, 17(4): 890–900 (2009)

    Article  Google Scholar 

  10. Takagi, T., Sugeno, M. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15(1): 116–132 (1985)

    Article  MATH  Google Scholar 

  11. Tian, E., Yue, D., Peng, C. Reliable control for networked control systems with probabilistic actuator fault and random delays. Journal of the Franklin Institute, 347(10): 1907–1926 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tian, E., Yue, D., Yang, T., Gu, Z., Lu, G. T-S fuzzy model-based robust stabilization for networked control systems with probabilistic sensor and actuator failure. IEEE Transactions on Fuzzy Systems, 19(3): 553–561 (2011)

    Article  Google Scholar 

  13. Tian, E., Yue, D., Zhang, Y. Delay-dependent robust H8 control for T–S fuzzy system with interval time-varying delay. Fuzzy sets and systems, 160(12): 1708–1719 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, H., Tanaka, K., Griffin, M. An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Transactions on Fuzzy Systems, 4(1): 14–23 (1996)

    Article  Google Scholar 

  15. Wang, Z., Ho, D., Liu, Y., Liu, X. Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements. Automatica, 45(3): 684–691 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wei, G., Wang, Z., Shu, H. Robust filtering with stochastic nonlinearities and multiple missing measurements. Automatica, 45(3): 836–841 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yang, F., Wang, Z., Ho, D., Gani M. Robust H∞ control with missing measurements and time delays. IEEE Transactions on Automatic Control, 52(9): 1666–1672 (2007)

    Article  MathSciNet  Google Scholar 

  18. Yoneyama, J. Robust stability and stabilization for uncertain Takagi–Sugeno fuzzy time-delay systems. Fuzzy Sets and Systems, 158(2): 115–134 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Yue, D., Lam, J., Ho, D. Reliable H∞ control of uncertain descriptor systems with multiple time delays. IET Control Theory and Applications, 150(6): 557–564 (2003)

    Article  Google Scholar 

  20. Zhang, D., Su, H., Pan, S., Chu, J., Wang, Z. LMI approach to reliable guaranteed cost control with multiple criteria constraints: The actuator faults case. International Journal of Robust and Nonlinear Control, 19(8): 884–899 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Southeast University, Nanjing, 210096, China

    Jin-liang Liu, Zhou Gu & Shu-min Fei

  2. College of Information Engineering, Nanjing University of Finance and Economics, Nanjing, 210023, China

    Jin-liang Liu

Authors
  1. Jin-liang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhou Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shu-min Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shu-min Fei.

Additional information

Supported by the National Natural Science Foundation of China (No. 61403185 and 71301100), the China Postdoctoral Science Foundation (No.2014M561558 and 2014M551487), the Postdoctoral Science Foundation of Jiangsu Province (No.1401005A and 1301009A), major project supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.15KJA120001), six talent peaks project in Jiangsu Province (No.2015-DZXX-021), Qing-Lan Project, Collaborative Innovation Center for Modern Grain Circulation and Safety, and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and Jiangsu Key Laboratory of Modern Logistics (Nanjing University of Finance & Economics).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Jl., Gu, Z. & Fei, Sm. Reliable control for nonlinear systems with stochastic actuators fault and random delays through a T-S fuzzy model approach. Acta Math. Appl. Sin. Engl. Ser. 32, 395–406 (2016). https://doi.org/10.1007/s10255-016-0566-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-016-0566-9

Keywords

2000 MR Subject Classification

Search

Navigation