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 cont...

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Bibliographic Details
Published in:Nonlinear analysis. Hybrid systems Vol. 22; pp. 31 - 42
Main Authors: Li, Shuo, Xiang, Zhengrong
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.11.2016
Subjects:
[formula omitted]-gain controller design
Linear programming
Markov jump systems
Positive systems
Stochastic stability
Time-varying delay
Positive systems
Linear programming
Stochastic stability
Markov jump systems
Time-varying delay
L∞-gain controller design
ISSN:1751-570X
Online Access:Get full text
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Summary: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.
ISSN:1751-570X
DOI:10.1016/j.nahs.2016.02.004