DocumentCode :
986816
Title :
Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties
Author :
He, Yong ; Wu, Min ; She, Jin-hua ; Liu, Guo-Ping
Author_Institution :
Sch. of Inf. Sci. & Eng., Central South Univ., Changsha, China
Volume :
49
Issue :
5
fYear :
2004
fDate :
5/1/2004 12:00:00 AM
Firstpage :
828
Lastpage :
832
Abstract :
This note concerns the problem of the robust stability of a linear system with a time-varying delay and polytopic-type uncertainties. In order to construct a parameter-dependent Lyapunov functional for the system, we first devised a new method of dealing with a time-delay system without uncertainties. In this method, the derivative terms of the state, which is in the derivative of the Lyapunov functional, are retained and some free weighting matrices are used to express the relationships among the system variables, and among the terms in the Leibniz-Newton formula. As a result, the Lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the Lyapunov functional. This method is then easily extended to a system with polytopic-type uncertainties. Numerical examples demonstrate the validity of the proposed criteria.
Keywords :
Lyapunov matrix equations; delays; linear systems; robust control; time-varying systems; Leibniz-Newton formula; Lyapunov matrices; linear systems; parameter-dependent Lyapunov functional; polytopic-type uncertainties; robust stability; time-delay systems; time-varying delay; Delay effects; Equations; Helium; Linear matrix inequalities; Linear systems; Robust stability; Systems biology; Time varying systems; Uncertain systems; Uncertainty; LMI; Linear matrix inequality; parameter-dependent Lyapunov functional; polytopic-type uncertainties; robust stability; time-varying delay;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2004.828317
Filename :
1299019
Link To Document :
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