Estimates for solutions of homogeneous time-delay systems: comparison of Lyapunov–Krasovskii and Lyapunov–Razumikhin techniques

In this contribution, the estimates for response of time-delay systems with nonlinear homogeneous right-hand side degree strictly greater than one are constructed. The existing results obtained via Lyapunov--Razumikhin approach reminded. Their proofs, revisited in appendix, lead to explicit expressions involved constants. Based on a recently introduced Lyapunov–Krasovskii functional and known domain attraction, we present new system response. Using same Lyapunov function Lyapunov–Razumikhin construction functional, compare both approaches discuss illustrative examples.