Novel stability conditions of linear time-varying impulsive positive systems based on indefinite Lyapunov functions *

Abstract

This paper investigates the global asymptotic stability of linear time-varying impulsive positive systems (IPSs). Several novel stability criteria of linear time-varying IPSs with different types of impulsive effects are proposed by constructing an indefinite time-varying copositive Lyapunov function. In particular, by using the maximum and average dwell time methods, we discuss the stability of the addressed system with destabilizing impulses and stabilizing impulses, respectively. Moreover, we consider a special case in which the continuous dynamic of the system is not asymptotically stable and the system may contain some destabilizing impulses, and give a slightly stricter stability criterion. Finally, two examples are given to validate the effectiveness of the obtained results.