Exponential stabilization for differential and integro-differential equations of second order with multiple retardations

Abstract This study addresses the exponential stabilization of second-order impulsive delay differential equations and impulsive integro-delay differential equations with finitely many constant delays via Lyapunov–Krasovskii functionals. Throughout the paper, four new theorems are established, providing sufficient conditions for the exponential stabilization of the considered impulsive problems. The findings in this paper generalize and strengthen known results, which are available in the relevant literature, thereby contributing to the ongoing development of the field. Finally, two illustrative examples are provided to highlight the applicability, efficacy, and advantages of the proposed results.