Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals

Alexandre Seuret (1) , Corentin Briat (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 D-BSSE - Department of Biosystems Science and Engineering [ETH Zürich]

The robust stability analysis of asynchronous and uncertain sampled-data systems with constant incremental input delay is addressed in the looped-functional framework. These functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete-time stability conditions in an affine way, enabling then the consideration of uncertain and time-varying systems. The stability conditions are obtained by first reformulating the sampled-data system as an impulsive system, and by then considering a tailored looped-functional along with Wirtinger's inequality, a recently introduced inequality that has been shown to be less conservative than Jensen's inequality. Several examples are given for illustration.

Mots clés: Sampled-data systems; impulsive systems; looped-functionals; incremental delay; LMI

Domaines: Automatique / Robotique

Alexandre Seuret, Corentin Briat. Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals. Automatica, 2015, Automatica, 55 (5), pp.274-278. ⟨10.1016/j.automatica.2015.03.015⟩. ⟨hal-01170887⟩