Stabilization of positive Markov jump systems

This paper is concerned with investigating the problems of stability and stabilization for positive Markov jump systems. A notion of mean stability is introduced, which is shown to be equivalent to the common notions of stochastic stability in the literature. Necessary and sufficient conditions of mean stability and stabilization are established for both continuous-time and discrete-time positive Markov jump systems. All the conditions are solvable in terms of standard linear programming. Numerical examples are given to illustrate the effectiveness and the merits of the proposed methods.