Exponential stability of switched nonlinear time-delay systems combining Lyapunov-Krasovskii, Halanay and Razumikhin approaches

Abstract

In this study, we propose novel methods to ensure the exponential stability of switched nonlinear time-delay systems based on Lyapunov-Krasovskii, Lyapunov-Halanay and Lyapunov-Razumikhin approaches. We derive new average dwell-time bounds to establish global exponential stability by integrating Lyapunov-Krasovskii functionals and Lyapunov-Halanay functions under specified compatibility conditions. These conditions require an interchange between Lyapunov-Krasovskii functionals and Lyapunov-Halanay functions, with bounded integral operators. Additionally, we extend Halanay's inequality to accommodate functions with growth, enabling its applicability to scenarios where growth is observed. Using the method in Loko etal (2024), we construct Lyapunov-Krasovskii functionals from Lyapunov-Razumikhin functions, to establish exponential stability within a constrained switching framework. Illustrative examples demonstrate the effectiveness of our methodologies in various scenarios involving discrete, distributed, and historywise delays, highlighting the applicability of the proposed techniques. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.