Robust stochastic stability of discrete-time linear systems with Markovian jumping parameters

Author

Benjelloun, K. ; Boukas, E.K. ; Shi, P.

Author_Institution

Mech. Eng. Dept., Ecole Polytech., Montreal, Que., Canada

Volume

1

fYear

1997

fDate

10-12 Dec 1997

Firstpage

559

Abstract

We study the problems of stability and stability robustness for a class of discrete-time linear systems with Markovian jumping parameters (DTLSMJP) with norm bounded uncertainties. A necessary and sufficient condition for stochastic stability is established using a Lyapunov exponent. The approach gives a direct expression of the second moment that allows us to conclude on the stochastic stability of the DTLSMJP in the mean-square sense. Under the assumption that the uncertainties are norm bounded a sufficient condition guaranteeing the robust stability of the uncertain discrete-time linear systems with Markovian jumping parameters (UDTLSMJP) is presented, and it is in terms of a set of coupled discrete-time algebraic Riccati equations

Keywords

Markov processes; Riccati equations; discrete time systems; linear systems; robust control; stochastic systems; uncertain systems; Lyapunov exponent; Markovian jumping parameters; coupled discrete-time algebraic Riccati equations; discrete-time linear systems; necessary and sufficient condition; norm bounded a sufficient condition; norm bounded uncertainties; robust stochastic stability; Control systems; Councils; Linear systems; Power system economics; Power system modeling; Robust stability; Stochastic processes; Stochastic systems; Sufficient conditions; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1997., Proceedings of the 36th IEEE Conference on

Conference_Location

San Diego, CA

ISSN

0191-2216

Print_ISBN

0-7803-4187-2

Type

conf

DOI

10.1109/CDC.1997.650689

Filename

650689