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Passivity Analysis and Passification of Markovian Jump Systems

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Abstract

This paper is concerned with the problems of delay-dependent robust passivity analysis and robust passification for uncertain Markovian jump linear systems (MJLSs) with time-varying delay. The parameter uncertainties are time varying but norm bounded. For the robust passivity problem, the objective is to seek conditions such that the closed-loop system under the state-feedback controller with given gains is passive, irrespective of all admissible parameter uncertainties. For the robust passification problem, desired passification controllers will be designed which guarantee that the closed-loop MJLS is passive. By constructing a proper stochastic Lyapunov–Krasovskii function and employing the free-weighting matrix technique, delay-dependent passivity/passification performance conditions are formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed approaches is demonstrated by a numerical example.

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Authors and Affiliations

  1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, P.R. China

    Xiuming Yao, Ligang Wu & Changhong Wang

  2. School of Control Science and Engineering, North China Electric Power University, Baoding, 071003, P.R. China

    Xiuming Yao

  3. School of Computing and Mathematics, University of Western Sydney, Penrith South DC, NSW, 1797, Australia

    Wei Xing Zheng

Authors
  1. Xiuming Yao
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  2. Ligang Wu
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  3. Wei Xing Zheng
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  4. Changhong Wang
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Corresponding author

Correspondence to Ligang Wu.

Additional information

This work was supported in part by the National Natural Science Foundation of China under Grants 60804002, the Natural Science Foundation of Heilongjiang Province of China (QC2009C58), the Program for New Century Excellent Talents in University, the Chinese National Post-doctor Science Foundation (20090460892), a research grant from the Australian Research Council and a research grant from the University of Western Sydney, Australia.

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Yao, X., Wu, L., Zheng, W.X. et al. Passivity Analysis and Passification of Markovian Jump Systems. Circuits Syst Signal Process 29, 709–725 (2010). https://doi.org/10.1007/s00034-010-9166-8

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  • DOI: https://doi.org/10.1007/s00034-010-9166-8

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