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| Received:October 08, 2003Revised:August 10, 2004 |
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| Parameter-dependent Lyapunov functional for systems with multiple time delays |
| Min Wu1,Yong He |
| (School of Information Science and Engineering, Central South University, 410083 Changsha Hunan, China ;School of Mathematical Science and Computing Technology, Central South University, 410083 Changsha Hunan, China) |
| Abstract: |
| The separation of the Lyapunov matrices and system matrices plays an important role when one uses parameter-dependent Lyapunov functional handling systems with polytopic type uncertainties. The delay-dependent robust stability problem for systems with polytopic type uncertainties is discussed by using parameter-dependent Lyapunov functional. The derivative term in the derivative of Lyapunov functional is reserved and the free weighting matrices are employed to express the relationship between die terms in the system equation such that the Lyapunov matrices are not involved in any product terms with the system matrices. In addition, the relationships between the terms in the Leibniz Newton formula are also described by some free weighting matrices and some delay-dependent stability conditions are derived. Numerical examples demonstrate that the proposed criteria are more effective than the previous results. |
| Key words: Robust stability Delay-dependent Parameter-dependent Lyapunov functional Polytopic type uncertainties Linear matrix inequality |
