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Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays

Author

Listed:
  • E. K. Boukas

    (École Polytechnique de Montréal)

  • Z. K. Liu

    (École Polytechnique de Montréal)

Abstract

This paper studies the class of uncertain linear systems with time delay and Markov jump disturbance, in which the time delay is assumed to be dependent on the system mode. An LMI-based condition for this class of systems to be robustly stable is established. Sufficient conditions for the robust stabilizability under a state feedback controller are developed, and an LMI-based method to design the state feedback is proposed. Numerical examples are worked out to show the usefulness of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:3:d:10.1023_a:1017515721760
    DOI: 10.1023/A:1017515721760
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    Cited by:

    1. 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.
    2. E. K. Boukas, 2008. "On State Feedback Stabilization of Singular Systems with Random Abrupt Changes," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 335-345, May.
    3. Yurong Liu & Yamin Wang & Xinquan Zhu & Xiaohui Liu, 2014. "Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1528-1538, July.

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