Abstract
This article investigates the stability and unweighted L1-gain analysis of switched time-delay positive systems (STDPSs) with stable and unstable subsystems. The persistent dwell time (PDT) switching is considered for the first time, which is more general compared with the typical dwell time (DT) or average dwell time (ADT) techniques. Under the PDT switching, the activation time of an unstable subsystem is less than an upper bound instead of greater than a given constant, which makes it easier to achieve stability in practice. Considering the stable and unstable subsystems, a piecewise multiple co-positive Lyapunov–Krasovskii functional is constructed to obtain the stability criterion of the STDPSs. Subsequently, the unweighted L1-gain for STDPSs is explored, which has explicit physical meaning compared with the weighted results and can be calculated by solving the linear programming problem. Finally, a water-quality model and a numerical example are provided to indicate the validity of the proposed methods.
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