Stochastic stability properties of jump linear systems

Author

Feng, Xiangbo ; Loparo, Kenneth A. ; Ji, Yuandong ; Chizeck, Howard Jay

Author_Institution

Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA

Volume

37

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

38

Lastpage

53

Abstract

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for δ-moment stability is monotonically converging to the region for almost sure stability at δ↓0⁺

Keywords

Lyapunov methods; control system analysis; linear systems; stability; Lyapunov exponent method; jump linear systems; necessary conditions; sample path stability; second moment stability; stochastic stability; sufficient condition; Control systems; Controllability; Linear systems; Optimal control; Stability; State feedback; Stochastic resonance; Stochastic systems; Sufficient conditions; Testing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.109637

Filename

109637