Stochastic stability analysis and L∞-gain controller design for positive Markov jump systems with time-varying delays. (November 2016)

• Record Type: Journal Article
• Authors: Li, Shuo; Xiang, Zhengrong
• Is Part Of: Nonlinear analysis. Volume 22(2016)
• Page Start: 31
• Page End: 42
• Publication Date: 2016-11
• Subjects: Positive systems -- Markov jump systems -- Stochastic stability -- L∞-gain controller design -- Time-varying delay -- Linear programming; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2016.02.004
• Languages: English
• ISSNs: 1751-570X

Abstract

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.