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\(\mathcal{H}_{\infty}\) Control Synthesis for Short-Time Markovian Jump Continuous-Time Linear Systems

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Abstract

In many actual engineering applications, the Markovian jump among subsystems often occurs in some short finite-time intervals. For this class of Markovian jump systems, called short-time Markovian jump systems in this paper, the state boundedness during the short-time Markovian jump interval is of great interest. By introducing the concepts of finite-time stochastic stability and boundedness, sufficient conditions ensuring short-time Markovian jump system to be \(\mathcal{H}_{\infty}\) finite-time stochastic bounded are derived. Then, the control synthesis problem is studied, where both asymptotic stability and finite-time stochastic boundedness are considered. Finally, an LMI-based design algorithm is proposed to solve the control synthesis problem. Several numerical examples are given to illustrate the results proposed in this paper.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants Nos. 51177137 and 61134001.

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Authors and Affiliations

  1. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, 610031, China

    Weiming Xiang

  2. School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031, China

    Jian Xiao & Lu Han

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  1. Weiming Xiang
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  2. Jian Xiao
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  3. Lu Han
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Correspondence to Weiming Xiang.

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Xiang, W., Xiao, J. & Han, L. \(\mathcal{H}_{\infty}\) Control Synthesis for Short-Time Markovian Jump Continuous-Time Linear Systems. Circuits Syst Signal Process 32, 2799–2820 (2013). https://doi.org/10.1007/s00034-013-9594-3

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  • DOI: https://doi.org/10.1007/s00034-013-9594-3

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