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**Robust reliable \(H_{\infty}\) control for nonlinear stochastic Markovian jump systems.**
*(English)*
Zbl 1264.93259

Summary: The robust reliable \(H_{\infty}\) 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 \(\alpha\) and disturbance attenuation \(\gamma\). 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 \(H_{\infty}\) controller for linear SMJSs and NSMJSs are given. Finally, a numerical example is exploited to show the usefulness of the derived results.

### MSC:

93E15 | Stochastic stability in control theory |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

60J27 | Continuous-time Markov processes on discrete state spaces |

93B36 | \(H^\infty\)-control |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

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\textit{G. Chen} and \textit{Y. Shen}, Math. Probl. Eng. 2012, Article ID 431576, 16 p. (2012; Zbl 1264.93259)

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### References:

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