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

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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.

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References

  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]

    Article  MathSciNet  MATH  Google Scholar 

  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]

    Article  MATH  Google Scholar 

  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]

    Article  MathSciNet  MATH  Google Scholar 

  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]

    Article  MATH  Google Scholar 

  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]

    Article  MathSciNet  MATH  Google Scholar 

  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]

    Article  MathSciNet  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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]

    Article  MathSciNet  MATH  Google Scholar 

  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]

    Article  Google Scholar 

  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]

    Article  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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]

    Article  MathSciNet  MATH  Google Scholar 

  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]

    Article  MathSciNet  MATH  Google Scholar 

  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]

    Article  Google Scholar 

  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]

    Article  Google Scholar 

  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.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics Science, Liaocheng University, Liaocheng, 252000, China

    Hui Gao, Jianwei Xia & Guangming Zhuang

Authors
  1. Hui Gao
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  2. Jianwei Xia
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  3. Guangming Zhuang
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Corresponding author

Correspondence to Jianwei Xia.

Additional information

Recommended by Associate Editor Young Ik Son under the direction of Editor Duk-Sun Shim. This work was supported by Natural Science Foundation of China (No. 61573177, 61603170 and 61773191); the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant (ZR2016JL025).

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Gao, H., Xia, J. & Zhuang, G. Robust Finite-time Extended Dissipative Control for a Class of Uncertain Switched Delay Systems. Int. J. Control Autom. Syst. 16, 1459–1468 (2018). https://doi.org/10.1007/s12555-017-0393-7

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  • DOI: https://doi.org/10.1007/s12555-017-0393-7

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