A Survey on Numerical Techniques for Stability Analysis of Time-Varying Delay System

Over the past few decades, the stability issues of linear time-varying delay systems have garnered significant attention in academia. Numerous studies have been reported in the literature, focusing on obtaining less conservative stability conditions expressed in the form of Linear Matrix Inequalities. This paper firstly provides an investigation into numerical techniques developed to estimate the upper bound of the single integral term arising from the time derivative of double integral Lyapunov-Krasovskii function (LKF) candidates. Secondly, employing various LKF selection methods and developed numerical techniques, this paper derives six stability criteria of a time-varying delay system. Finally, the effectiveness of various numerical techniques is analyzed and evaluated from the two representative numerical examples.