Parameter-Dependent Lyapunov Functional for Stability of Time-Delay Systems With Polytopic-Type Uncertainties
Authors:
- Jin-Hua SheJSJin-Hua She
- Guo-Ping LiuGuo-Ping Liu
Top Cited Papers
- 18 May 2004
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 49 (5) , 828-832
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
This publication has 25 references indexed in Scilit:
- Parameter dependent stability and stabilization of uncertain time-delay systemsIEEE Transactions on Automatic Control, 2003
- Delay-dependent robust stabilization of uncertain state-delayed systemsInternational Journal of Control, 2001
- Delay-dependent robust H∞ control of uncertain linear state-delayed systemsAutomatica, 1999
- A delay-dependent stability criterion for systems with uncertain time-invariant delaysIEEE Transactions on Automatic Control, 1999
- Delay-dependent robust stabilization of uncertain systems with multiple state delaysIEEE Transactions on Automatic Control, 1998
- On Delay-Dependent Stability and Decay Estimate for Uncertain Systems with Time-Varying DelayAutomatica, 1998
- Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approachIEEE Transactions on Automatic Control, 1997
- Memoryless H/sup ∞/ controllers for state delayed systemsIEEE Transactions on Automatic Control, 1994
- Robust stability of delay dependence for linear uncertain systemsIEEE Transactions on Automatic Control, 1992
- Criteria for asymptotic stability of linear time-delay systemsIEEE Transactions on Automatic Control, 1985