Lyapunov coupled equations for infinite jump linear systems

Author

Fragoso, Marcelo D. ; Baczynski, Jack

Author_Institution

Dept. of Syst. & Control, Nat. Lab. for Sci. Comput., Petropolis, Brazil

Volume

3

fYear

2000

fDate

2000

Firstpage

2349

Abstract

Deals with Lyapunov equations for continuous-time Markov jump linear systems (MJLS). We focus on the case in which the Markov chain has a countably infinite state space. It is shown that the infinite MJLS is stochastically stabilizable (SS) if and only if the associated countably infinite coupled Lyapunov equations have a unique norm bounded strictly positive solution. This result does not hold for mean square stabilizability (MSS), since SS and MSS are no longer equivalent in our set up. To some extent, tools from operator theory in Banach space and, in particular, from semigroup theory are the technical underpinning of the paper

Keywords

Lyapunov methods; Markov processes; continuous time systems; linear systems; stability; stochastic systems; Banach space; Lyapunov coupled equations; Markov chain; continuous-time Markov jump linear systems; countably infinite state space; infinite jump linear systems; operator theory; semigroup theory; stochastically stabilizable system; unique norm bounded strictly positive solution; Control systems; Equations; Lifting equipment; Linear systems; Markov processes; Roentgenium; Stability; State-space methods; Stochastic systems; Vents;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2000. Proceedings of the 39th IEEE Conference on

Conference_Location

Sydney, NSW

ISSN

0191-2216

Print_ISBN

0-7803-6638-7

Type

conf

DOI

10.1109/CDC.2000.914150

Filename

914150