Stability analysis for switched positive linear systems under state-dependent switching

Abstract

This paper addresses the state-dependent stability problem of switched positive linear systems. Some exponential stability criteria are established on the given partitions of the nonnegative state space. First, a exponential stability of systems without delays is established with the help of a single linear co-positive Lyapunov function. When this does not seem possible, we also prove the stability by using multiple linear co-positive Lyapunov functions. Moreover, we extend this result to the delayed systems in terms of the single and multiple linear co-positive Lyapunov functionals respectively. The proposed results can be applied to the general systems without any special restriction. Some numerical examples are given to illustrate the effectiveness of our results.