New Criteria For The Stability Of A Class Of Linear Systems With Time-varying Delay

Time delays exist in various types of systems that may cause system instability.The study of linear systems with time delays is of great significance.In order to study whether the time-delay systems are stable,stability criteria for such systems have been studied a lot.This article mainly studies the criteria for a class of time-delay systems.The specific contents are as follows:In the first part,this paper is concerned with the stability analysis problem of a linear system with time-varying delays.We use an improved triple-integral inequality and the reciprocally convex inequality to discuss sufficient conditions of asymptotical stability of a class of linear system with time-varying delays.A modified triple inequality is proposed first;then based on a newly introduced Lyapunov-Krasovskii functional,a stability criterion for the time-delay system is derived using the reciprocally convex inequality and the proposed triple-integral inequality.A numerical example shows that the proposed criterion is more conservative than some existing ones.In the second part,two cases of the time-varying delay are discussed,that is,the time-varying delay is either differentiable or just uniformly continuous,according to the linear systems with time-varying delay.First,an improved triple-integral inequality is proposed to estimate triple-integrals tightly.Then,by introducing two novel Lyapunov-Krasovskii functionals catering for two cases of time-varying delay,two sufficient conditions on stability,respectively,for the system under two cases of time-varying delay are derived using the improved triple-integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently.Finally,three numerical examples show that the obtained results outperform some existing ones.