Stability of systems with time-varying delay

Abstract

This paper presents a useful theoretical extension of the Lyapunov-Krasovskii's theory to analyse the exponential stability of differential equations with time-varying delay. The presented theoretical analysis allows establishing the coefficients of an upper exponential bound of the real response of a delayed system. In addition, we propose stability conditions -delay amplitude independent- applied to linear and non-linear systems with time-varying delay. Based on the Krasovskii-type functional, the proposed functionals incorporate information of the delayed system. The main motivation of this paper is to arrive at conditions of exponential stability that show directly the influence of the time-varying delay and the non-delayed dynamics on the real response of a delayed system. Theoretical results are tested through a numerical example.