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Converse Lyapunov-Krasovskii theorems for uncertain retarded differential equations

Ihab Haidar 1 Paolo Mason 1 Mario Sigalotti 2, 3 
3 GECO - Geometric Control Design
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : In this article we give a collection of converse Lyapunov–Krasovskii theorems for uncertain retarded differential equations. We show that the existence of a weakly-degenerate Lyapunov–Krasovskii functional is a necessary and sufficient condition for the global exponential stability of linear retarded functional differential equations. This is carried out using a switched system representation approach.
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https://hal.inria.fr/hal-00924252
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Submitted on : Friday, December 22, 2017 - 6:02:06 PM
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Ihab Haidar, Paolo Mason, Mario Sigalotti. Converse Lyapunov-Krasovskii theorems for uncertain retarded differential equations. Automatica, 2015, 62, pp.263-273. ⟨10.1016/j.automatica.2015.09.034⟩. ⟨hal-00924252v3⟩

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