Infinite Markov jump-bounded real lemma

A bounded real lemma is established, providing an equivalent condition to stochastic stability (SS) of a continuous-time infinite Markovian jump linear system (MJLS) with a prescribed L 2 -stochastic disturbance attenuation level γ in terms of existence of solutions to an infinite set of coupled lin...

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Bibliographic Details
Published in:Systems & control letters 2008, Vol.57 (1), p.64-70
Main Authors: Todorov, Marcos G., Fragoso, Marcelo D.
Format: Article
Language:English
Subjects:
Applied sciences
Bounded real lemma
Computer science
control theory
systems
Continuous-time linear system
Control system analysis
Control theory. Systems
Exact sciences and technology
Markovian jump system
Stochastic stability
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Summary:A bounded real lemma is established, providing an equivalent condition to stochastic stability (SS) of a continuous-time infinite Markovian jump linear system (MJLS) with a prescribed L 2 -stochastic disturbance attenuation level γ in terms of existence of solutions to an infinite set of coupled linear matrix inequalities (LMIs). Besides the interest in its own right, the main result provides a fundamental tool for the development of an H ∞ -like theory devoted to this class of systems.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2007.06.016