Exponential Mean Stability Analysis with Given Decay Rate and Resilient Controller Design for Positive Markov Jump Linear Systems

Abstract

For continuous-time positive Markov jump linear systems (MJLSs), exponential mean stability analysis and resilient controller design are studied. Necessary conditions of decay-rate-dependent exponential mean stability are proved by applying the available stochastic stability results of positive MJLSs, and the sufficiency is addressed by a linear stochastic co-positive Lyapunov function method. Based on the sufficient stability condition, linear programming conditions are proposed to ensure the existence of a resilient controller such that the closed-loop system is positive and exponentially mean stable. A numerical example for validation is finally provided.