New Results on Delay-dependent Robust Stability of Interval State-Delayed Linear Systems with Nonlinear Perturbations

Abstract

In this paper, we consider the problem of delay-dependent stability of a class of continuous-time and discrete-time linear systems with nonlinear perturbations and time-varying state-delays using Lyapunov functional approach. By exploiting candidate Lyapunov functionals, less conservative new robust stability criteria (sufficient conditions) are derived for computing the maximum allowable bound of the delay-range, within which, the uncertain systems under consideration remain asymptotically stable in the sense of Lyapunov. The proposed criteria are derived using reciprocal convex approach, and they are expressed as a set of solvable LMI conditions. The effectiveness of the proposed criteria are validated using standard numerical examples.