Resumen de Extensions of Razumikhin’s theorem and Lyapunov–Krasovskii functional constructions for time-varying systems with delay

Frederic Mazenc, Michael Malisoff

• Abstract 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.