Open AccessRobust stochastic stability and delayed‐state‐feedback stabilisation of uncertain Markovian jump linear systems with random time delays
Author(s) -
Qiu Li,
Shi Yang,
Xu Bugong,
Yao Fengqi
Publication year - 2015
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.2014.1138
Subject(s) - control theory (sociology) , markov process , linear matrix inequality , mathematics , stability (learning theory) , full state feedback , robust control , linear system , lyapunov function , state (computer science) , markov chain , controller (irrigation) , computer science , mathematical optimization , control system , control (management) , nonlinear system , engineering , algorithm , statistics , physics , quantum mechanics , artificial intelligence , machine learning , mathematical analysis , agronomy , electrical engineering , biology
The problem of robust stochastic stability and delayed‐state‐feedback stabilisation of uncertain Markovian jump linear systems with random Markov delays is investigated. Based on the Lyapunov stability theory and robust analysis techniques, some robust stochastic stability criteria are derived in terms of linear matrix inequalities. Robust delayed‐state‐feedback controllers that stochastically stabilise the uncertain Markovian jump linear systems is also proposed. The state variable on the controller is assumed to be dependent on the Markov delay that has uncertain transition probabilities. Finally, numerical examples are provided to illustrate the feasibility and effectiveness of the proposed methods.