Stochastic stability analysis and L∞-gain controller design for positive Markov jump systems with time-varying delays. (November 2016) - Li, Shuo; Xiang, Zhengrong
Abstract: 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.