Stochastic stability and stabilization of positive systems with Markovian jump parameters

This paper is concerned with stochastic stability and stabilization of positive systems with Markovian jump parameters in both continuous-time and discrete-time contexts. First, stochastic stability of the underlying systems in the autonomous case is discussed. Then, stochastic stabilization of non-autonomous systems is addressed, and mode-dependent state-feedback controllers are designed. All the proposed conditions are solvable in terms of linear programming with additional parameters. Finally, numerical examples are given to show the effectiveness of the present design.