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Stabilisation of descriptor Markovian jump systems with partially unknown transition probabilities

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  • Jinghao Li
  • Qingling Zhang
  • Xing-Gang Yan

Abstract

This paper is concerned with the stability and stabilisation problems for continuous-time descriptor Markovian jump systems with partially unknown transition probabilities. In terms of a set of coupled linear matrix inequalities (LMIs), a necessary and sufficient condition is firstly proposed, which ensures the systems to be regular, impulse-free and stochastically stable. Moreover, the corresponding necessary and sufficient condition on the existence of a mode-dependent state-feedback controller, which guarantees the closed-loop systems stochastically admissible by employing the LMI technique, is derived; the stabilizing state-feedback gain can also be expressed via solutions of the LMIs. Finally, numerical examples are given to demonstrate the validity of the proposed methods.

Suggested Citation

  • Jinghao Li & Qingling Zhang & Xing-Gang Yan, 2015. "Stabilisation of descriptor Markovian jump systems with partially unknown transition probabilities," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(2), pages 218-226, January.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:2:p:218-226
    DOI: 10.1080/00207721.2013.775394
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    Cited by:

    1. Gao, Xianwen & He, Hangfeng & Qi, Wenhai, 2017. "Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 431-441.
    2. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2016. "Asynchronous H∞ filtering for 2D discrete Markovian jump systems with sensor failure," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 60-79.
    3. Yingqi Zhang & Yan Shi & Xiaowu Mu & Caixia Liu, 2017. "control for conic non-linear jump systems with partially unknown transition probabilities," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 2976-2984, October.

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