Extensions of Razumikhin's theorem and Lyapunov-Krasovskii functional constructions for time-varying systems with delay

We prove extensions of Razumikhin's theorem for time-varying continuous and discrete time nonlinear systems. Our results include a novel 'strictification' technique for converting a nonstrict Lyapunov function into a strict one. We also provide new constructions of Lyapunov-Krasovskii functionals that can be used to prove robustness to perturbations. Our examples include a key model from identification theory, and they show how our method can sometimes allow broader classes of delays than the results in the literature. (C) 2016 Elsevier Ltd. All rights reserved.