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Asynchronous control for 2-D switched systems with mode-dependent average dwell time. (English) Zbl 1371.93073
Summary: This work is concerned with asynchronous control for a class of two-dimensional switched systems with mode-dependent average dwell time. The systems are formulated by the famous Fornasini-Marchesini local state-space model, and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems. By extending mode-dependent average dwell time with the switched quadratic Lyapunov functional approach, the stabilization condition is established for 2-D asynchronously switched systems. Based on the stabilization result, mode-dependent state-feedback controllers are designed to guarantee $$\mathcal{H}_\infty$$ performance and asymptotic stability of the corresponding closed-loop system. Finally, two examples are provided to illustrate the effectiveness of the proposed design scheme.

##### MSC:
 93B36 $$H^\infty$$-control 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D15 Stabilization of systems by feedback 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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