Stochastic Stability of Jump Discrete-Time Linear Systems With Markov Chain in a General Borel Space

Author

Costa, O.L.V. ; Figueiredo, D.Z.

Author_Institution

Dept. de Eng. de Telecomun. e Controle, Escola Politec. da Univ. de Sao Paulo, Sao Paulo, Brazil

Volume

59

Issue

1

fYear

2014

fDate

Jan. 2014

Firstpage

223

Lastpage

227

Abstract

Necessary and sufficient conditions for stochastic stability (SS) of discrete-time linear systems subject to Markov jumps in the parameters are considered, assuming that the Markov chain takes values in a general Borel space S. It is shown that SS is equivalent to the spectrum radius of a bounded linear operator in a Banach space being less than 1, or to the existence of a solution of a Lyapunov type equation. These results generalize several previous results in the literature, which considered only the case of the Markov chain taking values in a finite or infinite countable space.

Keywords

Banach spaces; Lyapunov matrix equations; Markov processes; discrete time systems; linear systems; stability; Banach space; Lyapunov type equation; Markov chain; Markov jumps; bounded linear operator; general Borel space; jump discrete-time linear system; spectrum radius; stochastic stability; General Borel space; Lyapunov equation; Markov jump linear systems; stochastic stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2270031

Filename

6544561