Delay-dependent stability and stabilisation of two-dimensional positive Markov jump systems with delays

This study considers the problem of exponential mean stability and stabilisation of two-dimensional positive Markov jump systems with delays. Necessary and sufficient delay-dependent conditions for exponential mean stability of the closed-loop system are first derived. Then, a design scheme based on...

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Bibliographic Details
Published in:IET control theory & applications 2017-06, Vol.11 (10), p.1603-1610
Main Authors: Van Hien, Le, Trinh, Hieu
Format: Article
Language:English
Subjects:
asymptotic stability
closed loop systems
closed‐loop system
delays
delay‐dependent stability
exponential mean stability
linear programming
linear programming problem
Markov jump systems
Markov processes
mode‐dependent controller
Research Article
stochastic systems
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Summary:This study considers the problem of exponential mean stability and stabilisation of two-dimensional positive Markov jump systems with delays. Necessary and sufficient delay-dependent conditions for exponential mean stability of the closed-loop system are first derived. Then, a design scheme based on a linear programming problem is proposed for obtaining parameters of a mode-dependent controller that makes the closed-loop system positive and exponentially mean stable. Finally, two numerical examples are presented to illustrate the effectiveness of the obtained results.
ISSN:1751-8644
1751-8652
1751-8652
DOI:10.1049/iet-cta.2016.1358