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Vol: 52(66) No: 3 / September 2007

Delay-range-dependent Stability for Systems with Time-varying Delay and Nonlinear Perturbations
Walid Kacem
UCA, Ecole Nationale d\'Ingénieurs de Sfax, ENIS, BP W, 3038, Sfax, Tunisia, phone: (216) 74 274088, e-mail: kacemwalid@yahoo.fr, web: www.enis.rnu.tn
Mohamed Chaabane
UCA, Ecole Nationale d\'Ingénieurs de Sfax, ENIS, BP W, 3038, Sfax, Tunisia, e-mail: mohamed.chaabane@ipeis.rnu.tn
Driss Mehdi
LAII, Ecole Supérieure d\'Ingénieurs de Poitiers, 40 Avenue du Recteur Pineau, Poitiers, France, e-mail: driss.mehdi@univ-poitiers.fr
Mohamed Kamoun
UCA, Ecole Nationale d\'Ingénieurs de Sfax, ENIS, BP W, 3038, Sfax, Tunisia, e-mail: mohamed.kamoun@enis.rnu.tn


Keywords: Time-delay systems, delay-dependent, robust stability, Linear Matrix Inequality, Nonlin-ear perturbations

Abstract
This paper deals with the robust stability of uncertain systems with time varying delay. The uncertainties under consideration are nonlinear perturbations. The time-delay is assumed to be a time-varying continuous function by taking into account that the lower and upper bounds for the time-varying delay are available and either with or without restriction on the derivative of the time-varying delay. The proposed delay dependent robust stability criterions are established based on Lyapunov functional and the Linear Matrix Inequality technique. Finally, numerical examples are given to demonstrate the effectiveness and the usefulness of the proposed method.

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