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Delay-dependent passivity and passification for uncertain Markovian jump systems with time-varying delays

Authors

  • Baoyong Zhang,

    1. School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu, China
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    • This work was done when Baoyong Zhang was with the School of Computing and Mathematics, University of Western Sydney, Penrith, NSW 2751, Australia.
  • Wei Xing Zheng,

    Corresponding author
    • School of Computing and Mathematics, University of Western Sydney, Penrith, NSW, Australia
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  • Shengyuan Xu

    1. School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu, China
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Wei Xing Zheng, School of Computing and Mathematics, University of Western Sydney, Penrith, NSW 2751, Australia.

E-mail: w.zheng@uws.edu.au

SUMMARY

This paper deals with the problems of passivity analysis and passivity-based controller design for Markovian jump systems with both time-varying delays and norm-bounded parametric uncertainties. Firstly, new delay-dependent conditions for the considered system to be passive are obtained by using a mode-dependent Lyapunov functional and by introducing some slack variables. These conditions are expressed by means of LMIs that are easy to check. It is shown through a numerical example that the obtained passivity conditions are less conservative than the existing ones in the literature. Secondly, the passification problem is investigated. On the basis of the obtained passivity conditions, dynamic output-feedback controllers are designed, which ensure that the resulting closed-loop system is passive. The effectiveness of the proposed design method is demonstrated by a numerical example. Copyright © 2011 John Wiley & Sons, Ltd.

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