Open AccessNew approach to delay‐dependent H ∞ filtering for discrete‐time Markovian jump systems with time‐varying delay and incomplete transition descriptions
Author(s) -
Wei Yanling,
Wang Mao,
Qiu Jianbin
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.2012.0621
Subject(s) - control theory (sociology) , mathematics , filter (signal processing) , lemma (botany) , discrete time and continuous time , markov process , linear matrix inequality , stability (learning theory) , filtering problem , bounded function , jump process , filter design , jump , computer science , mathematical optimization , mathematical analysis , control (management) , ecology , statistics , poaceae , artificial intelligence , machine learning , computer vision , biology , physics , quantum mechanics
This study is concerned with the delay‐dependent H ∞ filter design for a class of discrete‐time Markovian jump linear systems (MJLSs) with time‐varying delay and incomplete transition descriptions. The considered systems with incomplete transition descriptions cover the MJLSs with known transition probabilities (TPs), partially unknown TPs and uncertain TPs, which are more general. A new equivalent model is proposed for the original MJLSs by employing a two‐term approximation method, which formulates the filtering problem in the framework of input–output stability. Based on a Markovian Lyapunov–Krasovskii functional combined with the scaled small gain theorem, a new delay‐dependent bounded real lemma for the underlying systems is established. It is shown that by using a linearisation technique, the corresponding full‐ and reduced‐order H ∞ filter design is cast into a convex optimisation problem in terms of linear matrix inequalities. Finally, simulation examples are provided to illustrate the effectiveness and less conservatism of the proposed approach.