A New Relaxed Lyapunov-Krasovskii Functional for Stability Analysis of Time-Varying Delay Systems

Abstract

In this paper, the stability analysis problem of time-varying delay systems was studied. Based on recent research on Lyapunov-Krasovskii functionals (LKFs), relaxed conditions have been found to weaken some matrices in terms of LKFs, which means that some integral terms cannot be strictly positive definite. Therefore, motivate by this consideration, a new relaxed condition was constructed to weaken some matrices in constructed LKF. Then, for the sake of obtaining more information of time delays, dynamic delay interval (DDI) method was introduced to address the double integral terms with time-varying delay. Furthermore, some recent technologies were employed to process derivatives of LKF. As a consequence, a less conservative result was obtained. The examples given by previous papers were used to demonstrate the superiority of our work. INDEX TERMSRelaxed condition; Lyapunov-Krasovskii functional(LKF); stability analysis; timevarying delay systems.