Open AccessDelay‐dependent stability and stabilisation of two‐dimensional positive Markov jump systems with delays
Author(s) -
Van Hien Le,
Trinh Hieu
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.1358
Subject(s) - control theory (sociology) , mathematics , exponential stability , stability (learning theory) , exponential function , controller (irrigation) , jump , exponential growth , markov chain , mathematical optimization , computer science , control (management) , nonlinear system , mathematical analysis , statistics , physics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
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.