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

• Autores: Frederic Mazenc, Michael Malisoff
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 78, 2017, págs. 1-13
• Idioma: inglés
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• Resumen

  • 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.