Improved robust stability criteria for time delay systems with nonlinear perturbations

Abstract

In this paper, sufficient delay independent and delay-dependent robust stability criteria are introduced for a class of linear systems with nonlinear time-varying delayed perturbations. The conventional Lyapunov-Krasovskii functional is modified. The stability condition is formulated in the form of reduced dimensioned linear matrix inequalities (LMI). Moreover, a less conservative inequality is employed for bounding the cross-terms that involve parameter perturbations. In addition, a robust delay-dependent criterion is derived via using Leibniz-Newton model transformation and employing an arbitrary virtual state matrix on the delayed state. A recently given free weighting matrices approach is employed to further reduce the conservatism on the robustness of the delay bound. Numerical examples are given and the robust stability bounds are computed using LMI control toolbox. A brief comparison indicates that the proposed methods yield better results than those obtained with the existing methods.