Enhanced Impulsive Stabilization Results of Differential and Integro-Differential Equations of Second Order

Abstract

This paper delves into the exponential stabilization of delay differential equations (DDEs) and integro-delay differential equations (IDDEs) of second order including multiple constant retardations. By means of impulsive controls (ICs), we prove that the considered DDEs and IDDEs of second order can be exponentially stabilized. By defining two new Lyapunov-Krasovskiı̆ functionals (LKFs), we prove four new results on the exponential impulsive stabilization of the equations. Two examples are given to show numerical applications of the results. The results of this paper generalize and enhance some recent and related results in the literature. © 2025 Elsevier B.V., All rights reserved.