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 is 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 is 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 are employed to process derivatives of LKF. As a consequence, a less conservative result is obtained. The examples given by previous papers are used to demonstrate the superiority of our work.

Keywords

• Relaxed condition
• Lyapunov-Krasovskii functional (LKF)
• stability analysis
• time-varying delay systems