Delay-Dependent Stability, Integrability and Boundedeness Criteria for Delay Differential Systems

This paper deals with non-perturbed and perturbed systems of nonlinear differential systems of first order with multiple time-varying delays. Here, for the considered systems, easily verifiable and applicable uniformly asymptotic stability, integrability, and boundedness criteria are obtained via defining an appropriate Lyapunov–Krasovskiĭ functional (LKF) and using the Lyapunov– Krasovskiĭ method (LKM). Comparisons with a former result that can be found in the literature illustrate the novelty of the stability theorem and show new contributions to the qualitative theory of solutions. A discussion of two illustrative examples and the obtained results are presented.