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Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays

Author

Listed:
  • Quanxin Zhu

    (Ningbo University)

  • Fubao Xi

    (Beijing Institute of Technology)

  • Xiaodi Li

    (Shandong Normal University)

Abstract

In this paper, the problem of robust exponential stability is investigated for a class of stochastically nonlinear jump systems with mixed time delays. By applying the Lyapunov–Krasovskii functional and stochastic analysis theory as well as matrix inequality technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. Time delays proposed in this paper comprise both time-varying and distributed delays. Moreover, the derivatives of time-varying delays are not necessarily less than 1. The results obtained in this paper extend and improve those given in the literature. Finally, two numerical examples and their simulations are provided to show the effectiveness of the obtained results.

Suggested Citation

  • Quanxin Zhu & Fubao Xi & Xiaodi Li, 2012. "Robust Exponential Stability of Stochastically Nonlinear Jump Systems with Mixed Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 154-174, July.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:1:d:10.1007_s10957-012-9997-5
    DOI: 10.1007/s10957-012-9997-5
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    References listed on IDEAS

    as
    1. E. K. Boukas & Z. K. Liu, 2001. "Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 587-600, June.
    2. K. Benjelloun & E. K. Boukas & O. L. V. Costa, 2000. "H∞-Control for Linear Time-Delay Systems with Markovian Jumping Parameters," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 73-95, April.
    3. P. Shi & E. K. Boukas, 1997. "H ∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 75-99, October.
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    Cited by:

    1. Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.

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