## 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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### References:

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