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Impulsive effects on the stability and stabilization of positive systems with delays. (English) Zbl 1367.93560

Summary: This study addresses the exponential stability and positive stabilization problems of impulsive positive systems (IPSs) with time delay. Specially, three types of impulses, namely, disturbance, “neutral”, and stabilizing impulses, are considered. For each type of impulsive effect, the exponential stability criterion is established utilizing the Lyapunov-Razumikhin techniques. Moreover, on the basis of the obtained stability results, the state-feedback controller design problem is investigated to positively stabilize the IPSs with time delay under different types of impulsive effects. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.

MSC:

93D20 Asymptotic stability in control theory
93D21 Adaptive or robust stabilization
93B52 Feedback control
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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