Open AccessStabilisation of Markov jump linear systems subject to both state and mode detection delays
Author(s) -
Yang Ting,
Zhang Lixian,
Li Yuandi,
Leng Yusong
Publication year - 2014
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.2013.0507
Subject(s) - control theory (sociology) , lyapunov function , jump , linear system , mode (computer interface) , markov chain , state (computer science) , state space , mathematics , markov process , stability (learning theory) , computer science , nonlinear system , algorithm , control (management) , statistics , mathematical analysis , physics , quantum mechanics , artificial intelligence , machine learning , operating system
This study addresses the stabilisation problem of a class of discrete‐time Markov jump linear systems subject to time delays which occur in both the system state and mode detection. The mode detection delay means that there exists a lag between the switching of the system modes and the switching of the corresponding controllers. The state delays are considered to be random but with upper and lower bounds, and the mode detection delay is assumed to be constant. With an extended state space, the underlying system can be remodelled as a Markov jump linear system in which the system complexity and the number of system modes are both increased to a certain extent, but remain unchanged when the mode detection delay becomes larger. A sufficient condition guaranteeing the stochastic stability of the system is obtained via a modified stochastic Lyapunov function. The effectiveness of the proposed design approach is demonstrated by a numerical example.