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On State Feedback Stabilization of Singular Systems with Random Abrupt Changes

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  • E. K. Boukas

    (École Polytechnique de Montréal)

Abstract

This paper deals with the class of continuous-time singular linear systems with random abrupt changes. The state feedback stabilization and its robustness for this class of systems with norm-bounded uncertainties are tackled. Sufficient conditions for designing either a stabilizing controller or a robust stabilizing controller are developed in the LMI setting. The developed sufficient conditions are used to synthesize the state feedback controller that guarantees that either the nominal system or the uncertain system is piecewise regular, impulse free and stochastically stable or robust stochastically stable.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:2:d:10.1007_s10957-007-9338-2
    DOI: 10.1007/s10957-007-9338-2
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    References listed on IDEAS

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    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. 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.
    3. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

    1. Ma, Yuechao & Jia, Xiaorui & Liu, Deyou, 2016. "Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 213-227.
    2. Zhou Haiying & Zhu Huainian & Zhang Chengke, 2014. "Linear Quadratic Nash Differential Games of Stochastic Singular Systems," Journal of Systems Science and Information, De Gruyter, vol. 2(6), pages 553-560, December.

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