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Robust Finite-time Extended Dissipative Control for a Class of Uncertain Switched Delay Systems

  • Hui Gao
  • Jianwei Xia
  • Guangming Zhuang
Technical Notes and Correspondence
  • 54 Downloads

Abstract

This paper investigates the problem of finite-time extended dissipative analysis and control for a class of uncertain switched time delay systems, where the uncertainties satisfy the polytopic form. By using the average dwell-time and linear matrix inequality technique, some sufficient conditions are proposed to guarantee that the switched system is finite-time bounded and has finite-time extended dissipative performance, where the H, L2-L, Passivity and (Q, S, R)-dissipativity performance can be solved simultaneously in a unified framework based on the concept of extended dissipative. Furthermore, a state feedback controller is presented to guarantee that the closed-loop system is finite-time bounded and satisfies the extended dissipative performance. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Keywords

Average dwell-time extended dissipative finite-time switch time delay 

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References

  1. [1]
    H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Trans. Autom. Control, vol. 54, no. 2, pp. 308–322, 2009. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, pp. 59–70, 1999. [click]CrossRefzbMATHGoogle Scholar
  3. [3]
    X. D. Zhao, L. X. Zhang, P. Shi, and M. Liu, “Stability of switched positive linear systems with average dwell time switching,” Automatica, vol. 48, pp. 1132–1137, 2012. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    L. Lu, Z. L. Lin, and H. J. Fang, “L 2 gain analysis for a class of switched systems,” Automatica, vol. 45, pp. 965–972, 2009. [click]CrossRefzbMATHGoogle Scholar
  5. [5]
    X. D. Zhao, P. Shi, and L. X. Zhang, “Asynchronously switched control of a class of slowly switched linear systems,” Systems Control Letters, vol. 61, pp. 1151–1156, 2012. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    M. J. Hu, Y. W Wang, and J. W. Xiao, “Positive observer design for linear impulsive positive systems with interval uncertainties and time delay,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1032–1039, 2017. [click]MathSciNetCrossRefGoogle Scholar
  7. [7]
    Y. Zhang, H. Zhu, X. Liu, and S. Zhong. “Reliable H∞ control for a class of switched neutral systems,” Complex Syst Appl: Model. Control Simulat, vol. 14, no. S2, pp. 4–9, 2007.Google Scholar
  8. [8]
    D. Liu, S. Zhong, X. Liu, and Y. Huang. “Stability analysis for uncertain switched neutral systems with discrete timevarying delay: a delay-dependent method,” Math Comput Simulat., vol. 80, no. 8, pp. 28–39, 2009.CrossRefGoogle Scholar
  9. [9]
    L. Xiong, S. Zhong, M. Ye, and S. Wu. “New stability and stabilization for switched neutral control systems,” Chaos Solitons Fract, vol. 42. no. 3, pp. 1800–11, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    R. Wang, P. Shi, Z. G. Wu, and Y. T. Sun, “Stabilization of switched delay systems with polytopic uncertainties under asynchronous switching,” Journal of the Franklin Institute, vol. 350, pp. 2028–2043, 2013.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    X. Lin, H. Du, and S. Li. “Finite-time boundedness and L 2-gain analysis for switched delay systems with normbounded disturbance,” Appl Math Comput., vol. 217(12), no. 59, pp. 82–93, 2011.Google Scholar
  12. [12]
    Z. Xiang, Y. Sun, and M.S. Mahmoud, “Robust finite-time H∞ control for a class of uncertain switched neutral systems,” Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 4, pp. 1766–1778, 2012. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    S. Wang, T. G Shi, L. X. Zhang, A. Jasra, and M. Zeng, “Extended finite-time H∞ control for uncertain switched linear neutral systems with time-varying delays,” Neurocomputing, vol. 152, pp. 377–387, 2015. [click]CrossRefGoogle Scholar
  14. [14]
    S. Wang, M. Basin, L. X. Zhang, M. Zeng, T. Hayat, and A. Alsaedi, “Reliable finite-time filtering for impulsive switched linear systems with sensor failures,” Signal Processing, vol. 125, pp. 134–144, 2016. [click]CrossRefGoogle Scholar
  15. [15]
    B. Y. Zhang, W. X. Zheng, and S. Y. Xu, “Filtering of Markovian jump delay systems based on a new performance index,” IEEE Trans. Circuits Syst. I Reg. Pap., vol. 60, pp. 1250–1263, 2013.MathSciNetCrossRefGoogle Scholar
  16. [16]
    H. Shen, Y. Z. Zhu, L. X. Zhang, and J. H. Park, “Extended dissipative state estimation for Markov jump neural networks with unreliable links,” IEEE Trans. Neural Netw. Learning Syst., vol. 28, pp. 346–358, 2017.MathSciNetCrossRefGoogle Scholar
  17. [17]
    J. Y. Xiao, Y. T Li, S. M Zhong, F Xu, et al., “Extended dissipative state estimation for memristive neural networks with time-varying delay,” ISA Transactions, vol. 64, pp. 113–128, 2016.CrossRefGoogle Scholar
  18. [18]
    J. W. Xia, G. L. Chen, and W. Sun, “Extended dissipative analysis of generalized Markovian switching neural networks with two delay components,” Neurocomputing, vol. 260, pp. 275–283, 2017.CrossRefGoogle Scholar
  19. [19]
    H. L. Yang, L. Shu, S. M. Zhong, and X. Wang, “Extended dissipative exponential synchronization of complex dynamical systems with coupling delay and sampled-data control,” Journal of the Franklin Institute, vol. 353, pp. 1829–1847, 2016. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    H. B. Zeng, K. L Teo, and Y. He, “A new looped-functional for stability analysis of sampled-data systems,” Automatica, vol. 82, pp. 328–331, 2017. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    S. P. Xiao, X. Z. Liu, C. F. Zhang, and H. B. Zeng, “Further results on absolute stability of Lur’e systems with a time-varying delay,” Neurocomputing, vol. 207, pp. 823–827, 2016. [click]CrossRefGoogle Scholar
  22. [22]
    H. B. Zeng, Y. He, P. Shi, M. Wu, and S. P. Xiao, “Dissipativity analysis of neural networks with time-varying delays,” Neurocomputing, vol. 168, pp. 741–746, 2015. [click]CrossRefGoogle Scholar
  23. [23]
    S. P. Xiao, H. H. Lian, H. B. Zeng, G. Chen, and W. H. Zheng, “Analysis on robust passivity of uncertain neural networks with time-varying delays via free-matrix-based integral inequality,” International Journal of Control, Automation and Systems, vol. 15, pp. 1–10, 2017.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics ScienceLiaocheng UniversityLiaochengChina

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