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IMA Journal of Mathematical Control and Information Advance Access originally published online on November 4, 2005
IMA Journal of Mathematical Control and Information 2006 23(2):165-179; doi:10.1093/imamci/dni051
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A new Lyapunov technique for robust control of systems with uncertain non-small delays

Emilia Fridman**

Department of Electrical Engineering-Systems, Tel-Aviv University, Tel-Aviv 69978, Israel

** Email: emilia{at}eng.tau.ac.il

Stability, L2-gain analysis and state-feedback H{infty} control of linear systems with uncertain time-varying delays are considered in the case, where the nominal values of delays are constant and non-zero. A new construction of Lyapunov–Krasovskii functionals (LKFs) is introduced: to a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present paper we apply the nominal Lyapunov–Krasovskii functional (LKF) which is based on the descriptor model transformation. Sufficient conditions are given in terms of linear matrix inequalities. Numerical examples illustrate the efficiency of the method.

Keywords: uncertain delay; Lyapunov–Krasovskii method; stability; LMI; H{infty} control.

Received on 27 October 2004. accepted on 2 March 2005.


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