A General Formula for the Stabilization of Event-Based Controlled Systems

Nicolas Marchand (1) , Sylvain Durand (2) , Fermi Guerrero-Castellanos (3)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 NECS - Networked Controlled Systems
3 FCE BUAP - Facultad de Ciencias de la Electrónica [Puebla]

In this paper, a universal formula is proposed for event-based stabilization of general nonlinear systems affine in the control. The feedback is derived from the original one proposed by Sontag. Under the assumption of the existence of a smooth Control Lyapunov Function, it enables smooth (except at the origin) global asymptotic stabilization of the origin while ensuring that the sampling interval do not contract to zero. Indeed, for any initial condition within any given closed set the minimal sampling interval is proved to be strictly positive. Under homogeneity assumptions the control can be proved to be smooth anywhere and the sampling intervals bounded below for any initial condition.

Domaines: Automatique / Robotique

Nicolas Marchand, Sylvain Durand, Fermi Guerrero-Castellanos. A General Formula for the Stabilization of Event-Based Controlled Systems. CDC 2011 - ECC 2011 - 50th IEEE Conference on Decision and Control and European Control Conference, Dec 2011, Orlando, Floride, United States. Paper ThC16.5. ⟨hal-00648230⟩