STABILITY PROPERTY OF IMPULSIVE FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH FINITE DELAYS

Abstract

This study investigates the stability properties of impulsive functional differential inclusions with finite delays, a class of mathematical models that encapsulate dynamic systems influenced by sudden changes (impulses) and time delays in their state variables. We begin by establishing a comprehensive framework for analyzing such inclusions, incorporating the classical theory of functional differential equations and the modern theory of inclusions. By employing advanced mathematical tools, including Lyapunov functions and the Razumikhin technique, uniform stability and uniform asymptotic stability of impulsive functional differential inclusions are obtained. We derive sufficient conditions for the stability of solutions under varying impulse magnitudes and delay intervals. The interplay between impulsive effects and delayed responses is explored, revealing critical insights into how these factors influence the overall stability of the system. Our findings are further illustrated through several examples, demonstrating the practical implications of the theoretical results. This research not only contributes to the existing literature on impulsive differential inclusions but also provides valuable guidance for the design and analysis of complex dynamic systems in fields such as control theory, biology, and engineering.