Skip to main content
SpringerLink
Log in

Robust \(H_{\infty }\) Control for Networked Switched Fuzzy Systems with Network-Induced Delays and Packet Dropout

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

A networked switched fuzzy system, as a special networked control system, is studied. Such a system with network-induced delays and packet dropout is represented as a switched fuzzy system with time-varying delays. For this system, we investigate a robust \(H_{\infty }\) control problem. The solvability for the \(H_{\infty }\) control problem of each fuzzy subsystem is not assumed. Based on the multiple Lyapunov functions method, a state feedback control law and a switching law are designed such that the robust \(H_{\infty }\) control problem of the closed-loop system is solvable. Meanwhile, Lyapunov–Krasovskii functionals and free-weighting matrices are taken to deal with the induced delay and packet dropout caused by network. Finally, an example is given to verify the effectiveness of the proposed approach.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. S. Boyd, L.E. Ghaoui, E. Feron, Linear Martix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)

  2. M.S. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. W. Deng, M. Fei, T-S fuzzy \(H_\infty \) control and numerical simulation of nonlinear networked control systems. J. Syst. Simul. 22(7), 1652 (2010)

    Google Scholar 

  4. J. Hespanha, P. Naghshtabrizi, Y. Xu, A survey of recent results in networked control systems. Proc. IEEE 95, 38–162 (2007)

    Article  Google Scholar 

  5. L. Hetel, J. Daafouz, C. Iung, LMI control design for a class of exponential uncertain systems with application to network controlled switched systems, in Proceedings of American Control Conference, (Marriott Marquis Hotel at Times Square, New York, 2007), pp. 1402–1406

  6. D. Liberzon, Switching in System and Control (Birkhauser, Boston, 2003)

    Book  Google Scholar 

  7. D. Ma, Z. Guo, G. M. Dimirovski, J. Zhao, Passive Control for Networked Switched Systems with Network-Induced Delays and Packet Dropout, in Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, People’s Republic of China, 2009

  8. MathWorks, Using MatlabCLMI Toolbox, Natick, NJ: The Mathworks

  9. K.S. Narendra, J. Balakrishnan, A common Lyapunov function for stable LTI systems with commuting A-Matrices. IEEE Trans. Autom. Control 39, 2469–2471 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. X.-M. Sun, G.-P. Liu, Wei Wang, David Rees, Stability analysis for systems with large delay period: a switching method. Int. J. Innov. Comput. Inf. Control 8(6), 4235–4247 (2012)

    Google Scholar 

  11. T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man. Cybern. 15(1), 116–132 (1985)

    Article  MATH  Google Scholar 

  12. K. Tanaka, H.O. Wang, Fuzzy Control System Design and Analysis: A Linear Matrix Inequality Approach (Wiley, Canada, 2001)

    Book  Google Scholar 

  13. S.C. Tong, H.H. Li, Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets Syst. 131(2), 165–184 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. H.O. Wang, K. Tanaka, M. Griffin, An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans. Fuzzy Syst 4(1), 14–23 (1996)

    Article  Google Scholar 

  15. J. Wang, D. Ma, J. Luo, J. Zhao, in Stabilization of a class of Networked Switched Fuzzy Systems, The 25th Chinese Control and Decision Conference (Guiyang, 2013), pp. 25–27

  16. R.J. Wang, Observer-based fuzzy control of fuzzy time-delay systems with parametric uncertainties. Int. J. Syst. Sci. 35(12), 671–683 (2004)

    Article  MATH  Google Scholar 

  17. W.J. Wang, C.C. Kao, C.S. Chen, Stabilization, estimation and robustness for large-scale time-delay systems. Control Theory Adv. Technol. 7, 569–585 (1991)

    MathSciNet  Google Scholar 

  18. T.C. Yang, Networked control system: a brief survey. IEE Proc. Control Theory Appl. 153(4), 403–412 (2006)

    Article  Google Scholar 

  19. L. Yu, Robust Control- A linear Matrix Inequality Approach (Tsinghua University Press, Beijing, 2002)

    Google Scholar 

  20. M. Yu, L. Wang, T. Chu, Sampled-data stabilisation of networked control systems with nonlinearity. IEE Proc. Control Theory Appl. 152(6), 609–614 (2005)

    Article  Google Scholar 

  21. J. Zhang, Z. Han, F. Zhu, J. Huang, Robust finite-time stability and stabilization of switched positive systems. IET Control Theory Appl. 8(1), 67–75 (2014)

    MATH  MathSciNet  Google Scholar 

  22. W. Zhang, M.S. Branicky, S.M. Phillips, Stability of networked control systems. IEEE Control Syst. Mag. 21(1), 84–99 (2001)

    Article  Google Scholar 

  23. J. Zhao, D.J. Hill, On stability, \(L_{2}\) -gain and \(H_\infty \) control for switched systems. Automatica 44, 1220–1232 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  24. X. Zhao, X. Liu, S. Yin, H. Li, Improved results on stability of continuous-time switched positive linear systems. Automatica 50(2), 614–621 (2014)

    Article  MathSciNet  Google Scholar 

  25. X. Zhao, Y. Liu, Stability of fuzzy uncertain networked systems based on controller switching. Control Instrum. Chem. Ind. 35(5), 24–26 (2008)

    Google Scholar 

  26. X. Zhao, S. Yin, H. Li, B. Niu, Switching stabilization for a class of slowly switched systems. IEEE Trans. Autom. Control (2014). doi:10.1109/TAC.2014.2322961

  27. X. Zhao, L. Zhang, P. Shi, H.R. Karimi, Novel stability criteria for T–S fuzzy systems. IEEE Trans. Fuzzy Syst 22(2), 313–323 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants 61233002 and 61174073, and IAPI Fundamental Research Funds under Grant 2013ZCX03-01.

Author information

Authors and Affiliations

  1. State Key Laboratory of Synthetical Automation for Process Industries (Northeastern University), College of Information Science and Engineering, Northeastern University, Shenyang , 110819, People’s Republic of China

    Jinming Luo & Jun Zhao

Authors
  1. Jinming Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, J., Zhao, J. Robust \(H_{\infty }\) Control for Networked Switched Fuzzy Systems with Network-Induced Delays and Packet Dropout. Circuits Syst Signal Process 34, 663–679 (2015). https://doi.org/10.1007/s00034-014-9860-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9860-z

Keywords

Search

Navigation