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Robust Reliable ð » âˆž Control for Nonlinear Stochastic Markovian Jump Systems

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  • Guici Chen
  • Yi Shen

Abstract

The robust reliable ð » âˆž control problem for a class of nonlinear stochastic Markovian jump systems (NSMJSs) is investigated. The system under consideration includes Itô-type stochastic disturbance, Markovian jumps, as well as sector-bounded nonlinearities and norm-bounded stochastic nonlinearities. Our aim is to design a controller such that, for possible actuator failures, the closed-loop stochastic Markovian jump system is exponential mean-square stable with convergence rate ð ›¼ and disturbance attenuation ð ›¾ . Based on the Lyapunov stability theory and Itô differential rule, together with LMIs techniques, a sufficient condition for stochastic systems is first established in Lemma 3. Then, using the lemma, the sufficient conditions of the solvability of the robust reliable ð » âˆž controller for linear SMJSs and NSMJSs are given. Finally, a numerical example is exploited to show the usefulness of the derived results.

Suggested Citation

  • Guici Chen & Yi Shen, 2012. "Robust Reliable ð » âˆž Control for Nonlinear Stochastic Markovian Jump Systems," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-16, May.
    • Handle: RePEc:hin:jnlmpe:431576
    DOI: 10.1155/2012/431576
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    Cited by:

    1. Du, Yuanhua & Liu, Xinzhi & Zhong, Shouming, 2016. "Robust reliable H∞ control for neural networks with mixed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 1-8.

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