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Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay

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  • Control Theory and Applications
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Abstract

This paper is concerned with the problem of robust finite-time guaranteed cost control for a class of impulsive switched systems with time-varying delay. Firstly, the definitions of finite-time boundedness, finite-time stabilization, and robust finite-time guaranteed cost control are presented. Next, based on the average dwell-time approach, sufficient conditions on robust finite-time guaranteed cost control are obtained for the uncertain impulsive switched systems. Then, by using multiple Lyapunov-like functional method and linear matrix equality (LMI) technique, the state feedback controller is designed to guarantee that the uncertain impulsive switched system is finite-time stabilized. Furthermore, a finite-time guaranteed cost bound is given. Finally, a numerical example is shown to illustrate the effectiveness of the proposed results.

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References

  1. D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59–70, 1999.

    Article  Google Scholar 

  2. H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009.

    Article  MathSciNet  Google Scholar 

  3. G. D. Zong, L. L. Hou, and Y. Q. Wu, “Robust L 2–L ∞ guaranteed cost filtering for uncertain discrete-time switched system with mode-dependent time-varying delays,” Circuits Systems, and Signal Process, vol. 30, no. 1, pp. 17–33, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. P. Hespanha and A. S. Morse, “Stability of switched systems with average dwell-time,” Proc. 38th IEEE Conference Decision and Control, Phoenix, Arizona, pp. 2655–2660, 1999.

    Google Scholar 

  5. R. A. Decarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, “Perspectives and results on the stability and stabilizability of hybrid systems,” Proceedings of IEEE vol. 88, no. 7, pp. 1069–1082, 2000.

    Article  Google Scholar 

  6. F. Amato and M. Ariola, “Finite-time control of discretetime linear system,” IEEE Transaction on Automatic Control, vol. 50, no. 5, pp. 724–729, 2005.

    Article  MathSciNet  Google Scholar 

  7. F. Amato, A. Merola, and C. Cosentino, “Finite-time stability of linear time-varying systems: analysis and controller design,” IEEE Transactionson Automatic Control, vol. 55, no. 4, pp. 1003–1008, 2010.

    Article  MathSciNet  Google Scholar 

  8. G. D. Zong, R. H. Wang, W. X. Zheng, and L. L. Hou, “Finite-time H ∞ control for discrete-time switched nonlinear systems with time delay,” International Journal of Robust and Nonlinear Control, vol. 25, no. 6, pp. 914C936, 2015.

    Article  MathSciNet  Google Scholar 

  9. G. D. Zong, R. H. Wang, W. X. Zheng, and L. L. Hou, “Finite-time stabilization for a class of switched timedelay systems under asynchronous switching,” Applied Mathematics and Computation, vol. 219, no. 11, pp. 807–814, 2013.

    Article  MathSciNet  Google Scholar 

  10. X. Z. Lin, H. B. Du, and S. H. Li, “Finite-time boundedness and L 2-gain analysis for switched delay systems with norm-bounded disturbance,” Applied Mathematics and Computation, vol. 217, pp. 5982–5993, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Liu, Y. Shen, and X. D. Zhao, “Delay-dependent observer-based H ∞ finite-time control for switched systems with time-varying delay,” Nonlinear Analysis: Hybrid Systems, vol. 6, pp. 885–89, 2012.

    MathSciNet  MATH  Google Scholar 

  12. Y. J. Wang, X. M. Shi, Z. Q. Zuo, M. Z. Chen, and Y. T. Shao, “On finite-time stability for nonlinear impulsive switched systems,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 807–814, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Zhu, “Stability analysis of switched impulsive systems with time delays,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 3, pp. 608–617, 2010.

    MathSciNet  MATH  Google Scholar 

  14. H. L. Xu, X. Z. Liu, and K. L. Teo, “A LMI approach to stability analysis and synthesis of impulsive switched systems with time delays,” Nonlinear Analysis: Hybrid Systems, vol. 2, no. 1, pp. 38–50, 2008.

    MathSciNet  MATH  Google Scholar 

  15. Q. Wang and X. Z. Liu, “Stability criteria of a class of nonlinear impulsive switching systems with time-varying delays,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 1030–1047, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  16. Y. J. Wang, G. Wang, X. M. Shi, and Z. Q. Zuo, “Finitetime stability analysis of impulsive switched discrete-time linear systems: the average dwell time approach,” Circuits, Systems, and Signal Processing, vol. 31, no. 5, pp. 1877–1886, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  17. Z. G. Zhang, “Robust H ∞ control of a class of discrete impulsive switched systems,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, no. 12, pp. 2790–2796, 2009.

    Article  MathSciNet  Google Scholar 

  18. R. Wang and J. Zhao, “Non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems,” Journal of Control Theory and Applications, vol. 4, no. 1, pp. 32–37, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  19. R. Wang and J. Zhao, “Reliable guaranteed cost control for uncertain switched non-linear systems,” International Journal of Systems Science, vol. 40, no. 3, pp. 205–211, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  20. L. L. Hou, G. D. Zong, Y. Q. Wu, “Finite-time control for discrete-time switched systems with time delay,” International Journal of Control, Automation and Systems, vol. 10, no. 4, pp. 855–860, 2012.

    Article  Google Scholar 

  21. H. Xu, K. L. Teo, and X. Liu, “Robust stability analysis of guaranteed cost control for impulsive switched systems,” IEEE Trans Syst Man Cybern B Cybern, vol. 38, no. 5, pp. 1419–22, 2008.

    Article  Google Scholar 

  22. J. Gao, C. Liu, and Z. R. Xiang, “Robust Finite-Time H ∞ Control for Impulsive Nonlinear System with State Delay,” Mathematical Problems in Engineering, pp. 1–25, 2012.

    Google Scholar 

  23. X. M. Zhang and Q. L. Han, “Network-based H ∞ filtering using a logic jumping-like trigger,” Automatica, vol. 49, no. 5, pp. 1428–1435, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  24. X. M. Zhang and Q. L. Han, “Event-based H ∞ filtering for sampled-data systems,” Automatica, vol. 51, pp. 55–69, 2015.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Engineering, Qufu Normal University, Rizhao, 276826, P. R. China

    Guangdeng Zong, Xiaohong Wang & Haijuan Zhao

Authors
  1. Guangdeng Zong
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  2. Xiaohong Wang
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  3. Haijuan Zhao
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Corresponding author

Correspondence to Guangdeng Zong.

Additional information

Recommended by Associate Editor Mohammed Chadli under the direction of Editor Ju Hyun Park. This work is supported in part by National Natural Science Foundation (61273123, 61304153,61374004), in part by Program for New Century Excellent Talents in University NCET-13-0878, and in part by Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province.

Guangdeng Zong received his Ph.D. degree in control theory and application from Southeast University, Nanjing, China in 2005. His major research interests include network control, switched systems and robust control. He is currently a full professor in School of Engineering at Qufu Normal University.

Xiaohong Wang was born in Shandong Province, China in 1989. She received the Master’s degree in Operational Research and Cybernetics from Qufu Normal University in 2014. Now she is pursuing a Doctor’s degree in Control Science and Engineering from Southeast University, Nanjing, China. Her research interests include switched systems, nonsmooth control and time-delay systems.

Haijuan Zhao was born in Shandong Province, China, in 1990. She is currently pursuing the Master’s degree at the Institute of Automation, Qufu Normal University, Qufu, China. Her current research interests include switched systems, input-tostate stability and hybird systems.

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Zong, G., Wang, X. & Zhao, H. Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay. Int. J. Control Autom. Syst. 15, 113–121 (2017). https://doi.org/10.1007/s12555-015-0314-6

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  • DOI: https://doi.org/10.1007/s12555-015-0314-6

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