Exponential stability of impulsive positive systems with mixed time‐varying delays

Abstract

This study addresses the problem of exponential stability for a class of impulsive positive systems with mixed time‐varying delays. A delayed impulsive positive system model is introduced for the first time and a necessary and sufficient condition guaranteeing the positivity of this kind of system is proposed. By using a copositive Lyapunov–Krasovskii functional and the average impulsive interval method, a sufficient criterion of global exponential stability for delayed impulsive positive systems is established in terms of linear programming problems. A numerical example is given to show the effectiveness of the proposed method.