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\(L_1\) Control for Positive Markovian Jump Systems with Time-Varying Delays and Partly Known Transition Rates

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Abstract

This paper deals with the problem of \(L_1\) control for positive Markovian jump systems with time-varying delays and partly known transition rates. Firstly, by the use of appropriate co-positive type Lyapunov function, sufficient conditions for stochastic stability of positive Markovian jump systems with time-varying delays and partly known transition rates are proposed. Then, \(L_1\)-gain performance of the system considered is analyzed. Based on the results obtained, a state feedback controller is constructed such that the closed-loop Markovian jump system is positive and stochastically stable with \(L_1\)-gain performance. All the proposed conditions are derived in linear programming. Finally, an example is given to demonstrate the validity of the main results.

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Acknowledgments

This work is supported by Key Program of National Natural Science Foundation of China under Grant Nos. 61034005 and 61473097.

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  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Wenhai Qi & Xianwen Gao

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  1. Wenhai Qi
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  2. Xianwen Gao
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Correspondence to Xianwen Gao.

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Qi, W., Gao, X. \(L_1\) Control for Positive Markovian Jump Systems with Time-Varying Delays and Partly Known Transition Rates. Circuits Syst Signal Process 34, 2711–2726 (2015). https://doi.org/10.1007/s00034-015-9981-z

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  • DOI: https://doi.org/10.1007/s00034-015-9981-z

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