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Stability, $$L_1$$-gain and control synthesis for positive switched systems with time-varying delay. (English) Zbl 1287.93078
Summary: Exponential stability, $$L_1$$-gain performance and controller design problems for a class of positive switched systems with time-varying delay are investigated in this paper. First, by constructing an appropriate co-positive type Lyapunov-Krasovskii functional, sufficient conditions for the exponential stability are developed by using the average dwell time approach. Then, the weighted $$L_1$$-gain performance is investigated for the system considered. Based on the results obtained, an effective method is proposed for the construction of a stabilizing feedback controller with $$L_1$$-gain property. All the results are formulated as a set of Linear Matrix Inequalities (LMIs) and therefore can be easily implemented. Finally, the theoretical results obtained are demonstrated by a numerical example.

##### MSC:
 93D20 Asymptotic stability in control theory 93D30 Lyapunov and storage functions 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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