Robust stability of time delay systems with nonlinear perturbations

Abstract

In this paper the robust stability of a class of delayed systems with nonlinear time-varying parameter perturbations is investigated. Based on the Lyapunov stability method and quadratic stability theory, some novel delay-dependent robust stability criteria are derived. Unlike some existing methods, the main distinguishing feature of the proposed method is that any bounding of the cross-terms are not used in the stability analysis. This allows the newly obtained stability criteria to provide less conservative results than that of reported methods which often employ strict bounding for the cross-terms. As the stability criteria are given in the form of linear matrix inequalities, they can be easily solved by using interior-point algorithms. This indicates that the proposed method does not require tuning of any parameters and/or matrices for which it is rather difficult to give an optimization algorithm. Several numerical examples are considered for the purpose of comparison with some previously reported stability results from the literature in order to illustrate the effectiveness of the proposed method.