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The analysis of global input-to-state stability for piecewise affine systems with time-delay

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Abstract

In this paper, global input-to-state stability (ISS) for discrete-time piecewise affine systems with time-delay are considered. Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhin and Lyapunov-Krasovskii methods are used. The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown, respectively.

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, PRC

    Xiao-Wu Mu & Yang Gao

  2. Department of Mathematics, Daqing Normal University, Daqing, 163712, PRC

    Yang Gao

Authors
  1. Xiao-Wu Mu
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  2. Yang Gao
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Correspondence to Yang Gao.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60874006) and Natural Science Foundation of Heilongjiang Province for Youth (No.QC2009C99).

Xiao-Wu Mu graduated from Beijing University, PRC in 1983. He received the M. Sc. and the Ph. D. degrees from Beijing University, PRC in 1988 and 1991, respectively. He is currently a professor in the Department of Mathematics, Zhengzhou University, PRC.

His research interests include nonlinear system, discontinuous dynamical system, and system stability theory.

Yang Gao graduated from Beihua University, PRC in 2003. He received the M. Sc. degree from Harbin Institute of Technology, Harbin, PRC in 2005. He is currently a lecturer of Daqing Normal University, PRC and a Ph. D. candidate in the Department of Mathematics, Zhengzhou University, PRC.

His research interests include nonlinear system, multi-agent system, and discontinuous dynamical system.

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Mu, XW., Gao, Y. The analysis of global input-to-state stability for piecewise affine systems with time-delay. Int. J. Autom. Comput. 9, 211–214 (2012). https://doi.org/10.1007/s11633-012-0635-3

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  • DOI: https://doi.org/10.1007/s11633-012-0635-3

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