## Reliable dissipative control for stochastic impulsive systems.(English)Zbl 1283.93258

Summary: This paper deals with the problem of reliable dissipative control for a class of stochastic hybrid systems. The systems under study are subject to Markovian jump, parameter uncertainties, possible actuator failure and impulsive effects, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback controllers and impulsive controllers such that, for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators, the stochastic hybrid system is stochastically robustly stable and strictly ($$Q,S,R$$)-dissipative. The sufficient conditions are obtained by using linear matrix inequality (LMI) techniques. The main results of this paper extend the existing results on $$H^{\infty}$$ control.

### MSC:

 93E03 Stochastic systems in control theory (general) 93B52 Feedback control 93E15 Stochastic stability in control theory 93D09 Robust stability
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### References:

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