A delay-derivative-dependent switched system model method for stability analysis of linear systems with time-varying delay☆

This paper addresses the issue of delay- and its derivative-dependent stability of a linear system with a time-varying delay. Based on the sign of the delay derivative, the time-varying delay is divided into two modes, namely a monotone increasing mode and a monotone decreasing mode. Then the original delay system is described as a switched system with two modes. This description motivates to construct a monotone-mode-based switching Lyapunov-Krasovskii functional, which allows different Lyapunov matrices for each mode in stability analysis of time-delay systems. By employing the average dwell time technique, several sufficient stability criteria are presented for the system under study. Over two extensively studied examples, we demonstrate that the proposed stability criteria can deliver larger delay upper bounds than some existing methods. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.