Abstract:
In the present article, we consider a class of systems of linear differential equations with infinite distributed delay and periodic coefficients. We use the Lyapunov–Krasovskii functional and obtain sufficient conditions for exponential stability of the zero solution, find conditions on perturbation of the coefficients of the system that guarantee preservation of exponential stability, and establish estimates for the norms of solutions of the initial and perturbed systems that characterize exponential decay at infinity.
Key words:
linear differential equations with distributed delay, periodic coefficients, stability, Lyapunov–Krasovskii functional.
This publication is cited in the following 1 articles:
A. Elmwafy, José J. Oliveira, César M. Silva, “Existence and exponential stability of a periodic solution of an infinite delay differential system with applications to Cohen–Grossberg neural networks”, Communications in Nonlinear Science and Numerical Simulation, 135 (2024), 108053