Stability analysis of systems with time-varying delays using overlapped switching Lyapunov Krasovskii functional

Abstract

This paper presents a new stability analysis approach for time-varying delay continuous systems which formulates the stability problem by presenting an overlapped switching Lyapunov Krasovskii functional (OSLKF). An exponential stability assessment method is proposed which considers two sets of conditions; local and discontinuity conditions. The local conditions establish the stability of the system based on the assumption that the delay parameters belong to a subdomain of the original domain. The discontinuity conditions are used to deal with the discontinuity issue of the switching Lyapunov functions at their switching points. These conditions have two major properties; it is not required that the time derivative of the delay to be less than unity and that the global exponential stability analysis of the model is possible. To illustrate the performance of the proposed method, two numerical examples are presented which demonstrate the effectiveness of the proposed approach as compared to the existing methodologies.