New Stability Analysis of a Time-Delay System Subject to Bounded Distributed Delay

Time-delay systems model various types of real systems. The problem of the time delay effect on the system performance, particularly its stability, is a recurring challenge. The presence of the time delay can lead to complex and disruptive behaviors, such as oscillations, poor performance, and instability. The Lyapunov method is widely used to analyze the stability of these systems by inferring stability conditions. In this paper, a simplified methodological approach for the stability analysis of distributed delay systems is proposed. This work aims to significantly reduce the complexity of calculations while preserving the rigor of classical methods based on the Lyapunov-Krasovskii functional, by utilizing Leibniz integrals. The study focuses on a linear system with state-distributed delay three numerical examples are used to verify the superiority of the stability conditions obtained in this work.