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Robust $$H_\infty$$ finite-time control for discrete-time polytopic uncertain switched linear systems. (English) Zbl 1388.93035
Summary: In this paper, the problem of the robust $$H_\infty$$ finite-time control is investigated for discrete-time polytopic uncertain switched linear systems. The parameter-dependent switched Lyapunov function approach is used to derive sufficient conditions that guarantee the systems to be robust $$H_\infty$$ finite-time bounded in terms of Linear Matrix Inequalities (LMIs). A striking feature is the use of scalar parameter that leads to LMI conditions that are less conservative than those of previously published conditions. Consequently, the reduced bound of the state trajectory and disturbance attenuation level can be obtained by searching for the optimal scalar value within a certain bound and solving a convex optimization problem. Furthermore, a new robust $$H_\infty$$ finite-time state-feedback controller is designed based on the proposed conditions. A numerical example is given to demonstrate the effectiveness of the proposed method.

MSC:
 93B36 $$H^\infty$$-control 93B35 Sensitivity (robustness) 93C55 Discrete-time control/observation systems 93C41 Control/observation systems with incomplete information 93C05 Linear systems in control theory
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