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Stabilization of continuous-time randomly switched systems via the LMI approach

Author

Listed:
  • Wang, Guoliang
  • Zhang, Qingling
  • Yang, Chunyu
  • Su, Chengli

Abstract

This paper is concerned on the stabilization problem of continuous-time switched systems with random switching signal where the dwell time in each subsystem consists of a fixed part and random part. New sufficient conditions for stabilizing controllers including mode-independent case are provided in terms of LMIs, which could be solved directly. Moreover, the obtained results are extended to a more general case that the corresponding operation mode of a controller experiences a disordering phenomenon. Without designing a controller depending on new operation modes (NOMs), a kind of controller only depending on the original operation modes (OOMs) is proposed and satisfies a minimum variance approximation, whose solvable conditions are also with LMI forms. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods.

Suggested Citation

  • Wang, Guoliang & Zhang, Qingling & Yang, Chunyu & Su, Chengli, 2015. "Stabilization of continuous-time randomly switched systems via the LMI approach," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 527-538.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:527-538
    DOI: 10.1016/j.amc.2015.05.061
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    References listed on IDEAS

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    1. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 100-120, October.
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    Cited by:

    1. Wang, Guoliang, 2016. "Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 155-170.
    2. Feng Zhao & Qingling Zhang & Guoliang Wang, 2016. "filtering for piecewise homogeneous Markovian jump nonlinear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(13), pages 3258-3271, October.

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