A new LMI condition for robust stability of discrete-time uncertain systems

In this paper, a new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine...

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Bibliographic Details
Published inSystems & control letters Vol. 54; no. 12; pp. 1195 - 1203
Main Authors Kau, Shih-Wei, Liu, Yung-Sheng, Hong, Lin, Lee, Ching-Hsiang, Fang, Chun-Hsiung, Lee, Li
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.12.2005
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Control theory. Systems
Discrete-time systems
Exact sciences and technology
Linear matrix inequality
Parameter-dependent Lyapunov matrix
Polytopic uncertainty
Robust stability
Discrete-time systems
Linear matrix inequality
Parameter-dependent Lyapunov matrix
Robust stability
Polytopic uncertainty
Robust control
Polytope
Uncertain system
Discrete time
Linear time
Lyapunov function
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Summary:In this paper, a new robust stability condition is derived for uncertain discrete-time linear systems with convex polytopic uncertainties. The condition is expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of uncertain systems easily by solving some LMIs. A rigorous proof is given to show that an interesting result appeared recently is a special case of the proposed condition. Numerical examples also demonstrate the merit of the present condition in the aspect of conservativeness over other results in the literature.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2005.04.007