Stability margin evaluation for uncertain linear systems

Author

Gong, C. ; Thompson, S.

Author_Institution

Dept. of Mech. & Manuf. Eng., Queen´´s Univ., Belfast, UK

Volume

39

Issue

3

fYear

1994

fDate

3/1/1994 12:00:00 AM

Firstpage

548

Lastpage

550

Abstract

A sufficient stability condition for parameter variation in a perturbed, continuous time, multivariable linear system, represented by a state space model is presented. Starting with the existence of an algebraic Riccati equation, a stability bound is derived from the polar decomposition of the nominal system matrix. Unlike previous work, the results are not dependent on the solution of the Lyapunov equation and, consequently, not a function of an arbitrarily selected positive definite matrix. In addition, the bound would appear to be the tightest possible, in that violation of the presented inequality can be shown to lead to instability

Keywords

linear systems; multivariable control systems; stability criteria; state-space methods; Lyapunov equation; algebraic Riccati equation; existence; nominal system matrix; parameter variation; perturbed continuous-time multivariable linear system; polar decomposition; positive definite matrix; stability bound; stability condition; stability margin evaluation; state space model; uncertain linear systems; Linear matrix inequalities; Linear systems; Matrix decomposition; Power system modeling; Riccati equations; Robustness; Stability; State-space methods; Symmetric matrices; Transfer functions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.280755

Filename

280755