Stability analysis of positive systems with delayed impulses

Abstract

This paper investigates the problem of the stability analysis for positive systems with stabilizing delayed impulses. First, the stability analysis problem is considered for positive systems, where impulse delay is assumed to be deterministic and the method of average impulsive delay (AID) is used to handle the time-delay term in impulses. Then, the stability analysis problem is studied for positive systems with stochastic impulsive delay, and the case is considered where the impulse delay is satisfied by Markov chain. Further, the criteria ensuring the globally exponential stability and the stochastically exponential stability are derived. Finally, two illustrative examples are presented to show the validity of the obtained results.