On finite-time stability and stabilization of positive systems with impulses

Abstract

Abstract This study investigates finite-time stability and stabilization problems for positive systems with impulses. By constructing a time-varying copositive Lyapunov function and utilizing the average impulsive interval approach, the finite-time stability criterion is established for the first time by exposing different impulsive effects. The relationship between the impulses and the length of the finite time interval is revealed via both theoretical analysis and simulations. As an extension, the finite-time L 1 gain performance is also addressed. Based on the finite-time stability results, the finite-time controller design problem is studied to guarantee the positivity and finite-time stability of the corresponding closed-loop system. The obtained criteria can be checked by the linear programming method. Several numerical examples are provided to demonstrate the effectiveness of the theoretical results.