Stability, \(L_1\)-gain and control synthesis for positive switched systems with time-varying delay.

*(English)*Zbl 1287.93078Summary: 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 |

##### Keywords:

exponential stability; weighted \(L_1\)-gain; controller design; positive switched systems; time-varying delay
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\textit{M. Xiang} and \textit{Z. Xiang}, Nonlinear Anal., Hybrid Syst. 9, 9--17 (2013; Zbl 1287.93078)

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