Stability analysis of continuous-time systems with time-varying delay using new Lyapunov-Krasovskii functionals

This paper studies the stability of linear continuous-time systems with time-varying delay by employing new Lyapunov-Krasovskii functionals. Based on the new Lyapunov-Krasovskii functionals, more relaxed stability criteria are obtained. Firstly, in order to coordinate with the use of the third-order Bessel-Legendre inequality, a proper quadratic functional is constructed. Secondly, two couples of integral terms {∫t−htsx(s)ds,∫stx(s)ds} and {∫t−hMsx(s)ds,∫st−htx(s)ds} are involved in the integral functionals ∫t−htt(·)ds and ∫t−hMt−ht(·)ds, respectively, so that the coupling information between them can be fully utilized. Finally, two commonly-used numerical examples are given to demonstrate the effectiveness of the proposed method.