On the stability analysis of sampled-data systems with delays

Alexandre Seuret (1) , Corentin Briat (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

This chapter deals with the stability analysis of sampled-data systems with input delays. In this study, the sampling interval is assumed to be time-varying. We also consider the situation when the sampled control law of the continuous-time systems is a static state feedback control law which is not computed with the most recent sample of the state but with past samples. Thus, the resulting discretized system has become a system with a constant or time-varying delay. The stability analysis of such sampled-data systems is performed by the use of Lyapunov-Krasovskii functionals for discrete-time systems to account for the constant discrete-time delay together with the recent method based on looped-functional in order to ensure robustness with respect to variations in the sampling interval. The stability conditions are expressed in terms of Linear Matrix Inequalities (LMI) and are evaluated on several examples.

Mots clés: LMI.; Lyapunov functions; Looped functionals; Discrete-time systems; Sampled-data systems

Domaines: Automatique / Robotique

Alexandre Seuret, Corentin Briat. On the stability analysis of sampled-data systems with delays. Delays and Networked Control Systems, 6, Springer, pp.97-112, 2016, Advances in Delays and Dynamics, 978-3-319-32372-5. ⟨10.1007/978-3-319-32372-5⟩. ⟨hal-02057236⟩