Stability and L1-gain analysis of periodic piecewise positive systems with constant time delay

Abstract

This paper is concerned with the stability and L1-gain analysis of periodic piecewise positive systems with constant time delay. Lambda-exponential stability, which is applied to characterize the decay rates of the considered systems, is investigated first. A co-positive Lyapunov-Krasovskii functional is used to obtain a sufficient stability condition. The stability condition characterizes the convergent speed of the state by the system matrices and the size of the time delay. One can also apply the Lyapunov-Krasovskii functional to characterize the L1-gain of the systems. By taking advantage of the periodic property of the system, linear inequalities are employed to characterize the L1-gain, and an unweighted upper bound of the L1-gain of the system is given.