Stochastic stability analysis and L∞-gain controller design for positive Markov jump systems with time-varying delays

This paper is concerned with stochastic stability analysis and L∞-gain (also called L∞-induced norm) controller design for positive Markov jump systems (MJSs) in continuous-time context by means of a linear programming (LP) technique. Firstly, by introducing an equivalent deterministic positive continuous-time linear system, we propose necessary and sufficient conditions of stochastic stability with a prescribed L∞-gain performance in LP form for the underlying system. Then based on the obtained results, an effective method for designing a desired L∞-gain controller is established. All the proposed conditions are solvable in terms of LP with additional parameters. Finally, a numerical example is given to illustrate the effectiveness of the present method.