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State feedback control for Lurie networked control systems

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Abstract

The problem of the stability analysis and controller design for Lurie networked control systems (NCSs) is investigated, in which the network-induced delays and data dropout problems are simultaneously considered. By considering that the network-induced delays are assumed to be time-varying and bounded, and analyzing the relationship between the delay and its upper bound, employing a Lyapunov-Krasovskii function and an integral inequality approach, an improved stability criterion for NCSs is proposed. Furthermore, the resulting condition is extended to design a less conservative state feedback controller by employing an improved cone complementary linearization (ICCL) algorithm. Numerical examples are provided to show the effectiveness of the method.

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References

  1. LEE K C, LEE K, LEE M H. Worst case communication delay of real-time industrial switched ethernet with multiple levels [J]. IEEE Trans Industrial Electronics, 2006, 53(4): 1669–1676.

    Article  Google Scholar 

  2. HEAPANHA J, P NSGHSHTABRIZI, XU Y. A survey of recent results in networked control systems [J]. Proc IEEE, 2007, 95(1): 138–162.

    Article  Google Scholar 

  3. XIAO S P, ZHANG X M. New globally asymptotic stability criteria for delayed cellular neural networks [J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2009, 56(8): 659–663.

    Article  MathSciNet  Google Scholar 

  4. CHEN Gang, YANG Chun-hua, ZHU Hong-qiu. Analysis and synthesis for networked control systems with network-induced delay and data dropout problem [J]. Systems Engineering and Electronics, 2012, 34(2): 78–83.

    Google Scholar 

  5. HUANG Can, GUI Wei-hua, YANG Chun-hua. Design of decoupling smith control for multivariable system with time delays [J]. Journal of Central South University, 2011, 18(2): 473–478.

    Article  Google Scholar 

  6. ZENG H B, XIAO S P, LIU B. New stability criteria for recurrent neural networks with a time-varying delay [J]. International Journal of Automation and Computing, 2011, 8(1): 128–133.

    Article  Google Scholar 

  7. WANG Y. H control of networked control systems via LMI approach [J]. Int J Innovative Computing, Information and Control, 2007, 3: 343–352.

    Google Scholar 

  8. PENG C, TIAN Y C, TADE M O. State feedback controller design of networked control systems with interval time-varying delay and nonlinearity [J]. Int J Robust Non. Control, 2008, 18(12): 1285–1301.

    MathSciNet  Google Scholar 

  9. ZENG H B, HE Y, WU M, XIAO S P. Further results on absolute stability of Lurie system with interval time-varying delay [C]// The 24th CCDC. Taiyuan, 2012, 23–25.

  10. KIM D, LEE Y, KWON W, PARK H. Maximum allowable delay bounds of networked control systems [J]. Control Engineering Practice, 2003, 11(11): 1301–1313.

    Article  Google Scholar 

  11. NILSSON J. Real-Time control systems with delays [D]. Department. of Automatic Control, Lund Institute of Technology. 1998: 27–35.

  12. ZHANG W, BRANICKY M S, Phillips S M. Stability of networked control systems [J]. IEEE Control Syst Mag 2001, 21(2): 84–99.

    Article  Google Scholar 

  13. CLOOSTERMAN M, van de WOUOW N, HEEMELS M, NIJMEIJE H. Robust stability of networked control systems with time-varying network-induced delays [C]// Proc 45th Conf on Decision and Control, San Diego, CA, 2006: 4980–4985.

  14. HETEL L, DAAFOUZ J, IUNG C. Stabilization of arbitrary switched linear systems with unknown time-varying delays [J]. IEEE Trans Automat Control, 2006, 51(10): 1668–1674.

    Article  MathSciNet  Google Scholar 

  15. XIE G, WANG L. Stabilization of networked control systems with time-varying network-induced delay [C]// Proc 43rd IEEE Conf Decision and Control Paradise Island, Bahamas, 2004: 3551–3556.

  16. ZHANG W, BRANICKY M S, PHILLIPS S M. Stability of networked control systems [J]. IEEE Control Systems Magazine, 2001 (21): 84–99.

  17. WALSH G C, YE H, BUSHNELL L. Stability analysis of networked control systems [C]// Proc American Control Conf, San Diego, CA, 1999: 2876–2880.

  18. YUE D, HAN Q L, PENG C. State feedback controller design of networked control systems [J]. IEEE Trans Circuits Sys II, 2004, 51(11): 640–644.

    Article  Google Scholar 

  19. WU M, HE Y, SHE J H. New delay-dependent stability criteria and stabilizing method for neutral systems [J]. IEEE Trans Autom Control, 2004, 49(12): 2266–2271.

    Article  MathSciNet  Google Scholar 

  20. YUE D, HAN Q L, LAM J. Network-based robust H control of systems with uncertainty [J]. Automatica, 2005, 41(6): 999–1007.

    Article  MathSciNet  MATH  Google Scholar 

  21. HE Y, LIU G P, REES D, WU M. Improved stabilisation method for networked control systems [J]. IET Contr Theory Appl, 2007, 1(6): 1580–1585.

    Article  Google Scholar 

  22. HAO F, ZHAO X. Absolute stability of Lurie networked control systems [J]. Int J Robust Non Contr, 2010, 20(12): 1326–1337.

    MathSciNet  MATH  Google Scholar 

  23. MOON Y S, PARK P, KWON WH, LEE Y S. Delay-dependent robust stabilization of uncertain state-delayed systems [J]. Int J Control, 2001, 74(14): 1447–1455.

    Article  MathSciNet  MATH  Google Scholar 

  24. GHAOUI L E, OUSTRY F, AITRAMI M. A cone complementarity linearization algorithm for static output feedback and related problems [J]. IEEE Trans Autom Control, 1997, 42(4): 1171–1176.

    Article  MATH  Google Scholar 

  25. KHALIL H K. Nonlinear systems [M]. Upper Saddle River. NJ: Prentice-Hall, 1996: 45–148.

    Google Scholar 

  26. ZHANG X M, WU M, SHE J H. Delay-dependent stabilization of linear systems with time-varying state and input delays [J]. Automatica, 2005, 41(3): 1405–1412.

    Article  MathSciNet  MATH  Google Scholar 

  27. YUE D, TIAN E G, ZHANG Y J. A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay [J]. International Journal of Robust and Nonlinear Control, 2009, 19(13): 1493–1518.

    Article  MathSciNet  Google Scholar 

  28. BOYD S, GHAOUI L E, FERON E. Linear matrix inequality in system and control theory [M]. Philadelphia: SIAM SIAM Studies in Applied Mathematics., 1994:187–190.

    Book  Google Scholar 

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Correspondence to Hong-qiu Zhu  (朱红求).

Additional information

Foundation item: Project(61025015) supported by the National Natural Science Foundation of China for Distinguished Young Scholars; Project (IRT1044) supported by the Program for Changjiang Scholars and Innovative Research Team in University of China; Projects(61143004, 61203136, 61074067, 61273185) supported by the National Natural Science Foundation of China; Projects(12JJ4062, 11JJ2033) supported by the Natural Science Foundation of Hunan Province, China; Project(12C0078) supported by Hunan Provincial Department of Education, China

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Chen, G., Zhu, Hq., Yang, Ch. et al. State feedback control for Lurie networked control systems. J. Cent. South Univ. 19, 3510–3515 (2012). https://doi.org/10.1007/s11771-012-1436-0

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  • DOI: https://doi.org/10.1007/s11771-012-1436-0

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