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On Finite-Time Stochastic Stability and Stabilization of Markovian Jump Systems Subject to Partial Information on Transition Probabilities

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Abstract

The problems of finite-time stochastic stability and stabilization for a class of linear Markovian jump systems subject to partial information on transition probabilities are considered in this paper. By introducing the concept of finite-time stochastic stability for linear Markovian jump systems, a new method is proposed to ensure that the state trajectory remains in a bounded region of the state space in mean square sense over a pre-specified finite-time interval. Based on this stability result, the finite-time stochastic stabilization criterion is then given. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China No. 60774039, No. 60974024, No. 61074089, No. 61174129, Program for New Century Excellent Talents in University No. NCET-11-0379, and the Independent Innovation Foundation of Tianjin University.

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Authors and Affiliations

  1. Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072, P.R. China

    Zhiqiang Zuo, Hongchao Li, Yi Liu & Yijing Wang

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  1. Zhiqiang Zuo
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  2. Hongchao Li
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  3. Yi Liu
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  4. Yijing Wang
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Correspondence to Zhiqiang Zuo.

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Zuo, Z., Li, H., Liu, Y. et al. On Finite-Time Stochastic Stability and Stabilization of Markovian Jump Systems Subject to Partial Information on Transition Probabilities. Circuits Syst Signal Process 31, 1973–1983 (2012). https://doi.org/10.1007/s00034-012-9420-3

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  • DOI: https://doi.org/10.1007/s00034-012-9420-3

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