Open AccessSpectral characterisation for stability and stabilisation of linear stochastic systems with Markovian switching and its applications
Author(s) -
Sheng Li,
Gao Ming,
Zhang Weihai
Publication year - 2013
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.2012.0471
Subject(s) - stability (learning theory) , control theory (sociology) , mathematics , markov process , lyapunov function , linear system , spectrum (functional analysis) , stochastic process , computer science , nonlinear system , mathematical analysis , physics , control (management) , statistics , quantum mechanics , artificial intelligence , machine learning
This study is concerned with the stability analysis and stabilisation of linear stochastic systems with Markovian switching by using the spectral technique. The notion of spectrum for Markovian jump linear stochastic systems (MJLSSs) is introduced and the relationship between the spectrum and the asymptotical mean‐square stability is revealed. As applications, a necessary and sufficient condition for regional stability of MJLSSs and a result on generalised Lyapunov equations are derived. Examples are presented to illustrate the results established.