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Exponential p-stability of singularly perturbed impulsive stochastic delay differential systems

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Abstract

In this paper, we study singularly perturbed impulsive stochastic delay differential systems (SPISDDSs). By establishing an L-operator delay differential inequality and using the stochastic analysis technique, we obtain some sufficient conditions ensuring the exponential p-stability of any solution of SPISDDSs for sufficiently small ɛ > 0. The results extend and improve the earlier publications. An example is also discussed to illustrate the efficiency of the obtained results.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, 310023, China

    Liguang Xu

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  1. Liguang Xu
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Correspondence to Liguang Xu.

Additional information

Recommended by Editor Young Il Lee. The work is supported by National Natural Science Foundation of China under Grants 11101367 and 11026140. The author thanks the reviewers for their constructive suggestions and helpful comments.

Liguang Xu received his Ph.D. degree in Operational Research and Cybernetics from the College of Mathematics, Sichuan University, China. His current research interests include qualitative theory of stochastic and impulsive systems, delay differential systems, switched systems and neural networks.

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Xu, L. Exponential p-stability of singularly perturbed impulsive stochastic delay differential systems. Int. J. Control Autom. Syst. 9, 966–972 (2011). https://doi.org/10.1007/s12555-011-0518-3

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  • DOI: https://doi.org/10.1007/s12555-011-0518-3

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