Improved Lyapunov Functional for Stability Analysis in Delay-Differential Systems

This paper explores the stability of differential systems influenced by time delays, with a specific focus on situations where these delays change over time. Such systems often present analytical challenges due to the unpredictable nature of the delays. To tackle this, we introduce a new form of Lyapunov–Krasovskii functional, which leads to a refined condition for stability that depends directly on the characteristics of the delay. This condition is formulated using Linear Matrix Inequalities (LMIs), which offer a practical way to assess stability while maintaining a solid theoretical foundation. By modeling the effects of time-varying delays more accurately, the method contributes both to a deeper understanding of how such delays affect system behavior and to more reliable tools for analyzing systems where delays are a built-in feature that cannot be ignored.