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Mean-Square Exponential Stability and Stabilisation of Stochastic Singular Systems with Multiple Time-Varying Delays

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Abstract

The stability and stabilisation problems for a series of continuous stochastic singular systems with multiple time-varying delays are studied in this paper. First, a useful lemma is proposed and a delay-distribution-dependent Lyapunov functional is constructed. Then, a novel delay-distribution-dependent condition is given to ensure the unforced stochastic singular systems to be regular and impulse-free. The mean-square exponential stability of the whole system is guaranteed under the proposed lemma. As a result, a suitable feedback controller is designed via strict linear matrix inequality such that the system’s stabilisation problem is guaranteed. Finally, numerical examples are illustrated to show the proposed result are less conservative than the existing ones and the potential of such technology.

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Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper. This work was also supported by the National Natural Science Foundation of China (No. 61403113), by the Zhejiang Provincial Natural Science Foundation of China (No. LQ14F030010) and by the Scientific Research Foundation of Hangzhou Dianzi University (No. KYS065613036).

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Authors and Affiliations

  1. Institute of System Science and Control Engineering, School of Automation, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    Jian-Ning Li

  2. Institute of Automation, Zhejiang Sci-Tech University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Yibo Zhang

  3. Department of Mechanical Engineering, Dalhousie University, P.O. Box 15000, Halifax, NS, B3H 4R2, Canada

    Ya-Jun Pan

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  1. Jian-Ning Li
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  2. Yibo Zhang
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Correspondence to Jian-Ning Li.

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Li, JN., Zhang, Y. & Pan, YJ. Mean-Square Exponential Stability and Stabilisation of Stochastic Singular Systems with Multiple Time-Varying Delays. Circuits Syst Signal Process 34, 1187–1210 (2015). https://doi.org/10.1007/s00034-014-9893-3

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