## Robust $$H_\infty$$ stabilization for uncertain switched impulsive control systems with state delay: An LMI approach.(English)Zbl 1163.93386

Summary: This paper deals with the problem of robust $$H_\infty$$ state feedback stabilization for uncertain switched linear systems with state delay. The system under consideration involves time delay in the state, parameter uncertainties and nonlinear uncertainties. The parameter uncertainties are norm-bounded time-varying uncertainties which enter all the state matrices. The nonlinear uncertainties meet with the linear growth condition. In addition, the impulsive behavior is introduced into the given switched system, which results a novel class of hybrid and switched systems called switched impulsive control systems. Using the switched Lyapunov function approach, some sufficient conditions are developed to ensure the globally robust asymptotic stability and robust $$H_\infty$$ disturbance attenuation performance in terms of certain Linear Matrix Inequalities (LMIs). Not only the robustly stabilizing state feedback $$H_\infty$$ controller and impulsive controller, but also the stabilizing switching law can be constructed by using the corresponding feasible solution to the LMIs. Finally, the effectiveness of the algorithms is illustrated with an example.

### MSC:

 93D21 Adaptive or robust stabilization 93D15 Stabilization of systems by feedback 93C05 Linear systems in control theory 93B51 Design techniques (robust design, computer-aided design, etc.) 93B36 $$H^\infty$$-control
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### References:

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