Necessary and Sufficient Conditions for Stochastic Stability and Stabilization of Positive Systems With Two Independent Markov Processes

Abstract

This article proposes some necessary and sufficient conditions for stochastic stability and stabilization of both continuous-time and discrete-time positive systems with two Markov jumping parameters. These conditions can be numerically checked by using linear programming method, and they are demonstrated to be with less conservatism and less computing complexity than the LMI-based mean square stability conditions of general Markov jump linear systems. Moreover, the proposed conditions are scalable to positive systems with multiple Markov jumping parameters. Some numerical examples are given to confirm the effectiveness and the advantages of the proposed conditions.