Stability and stabilization for positive systems with semi-Markov switching

Abstract

In this article, the problems of mean stability analysis and control synthesis are studied for stochastic switching systems subject to positive constraint. Such a switching is governed by a semi-Markov process subject to a special non-exponential distribution. Considering a linear Lyapunov-Krasovskii function (LKF), necessary and sufficient conditions are proposed to realize mean stability for the open-loop system. Based on this, the solvability conditions for the desired stabilizing controller can be determined under a linear programming (LP) framework. Finally, the theoretical findings are illustrated by the virus mutation treatment model.