Stability of nonlinear systems by means of event-triggered sampling algorithms

International audienceIn this paper, the problem of feedback control implementation for nonlinear systems is considered. Some conditions for holding the same control input until an event occurs are derived. With respect to classical approaches, where feedback laws are implemented in a periodically fashion, it is suggested new algorithms to use the same control input. By means of these algorithms, some jumps of the control inputs occur and the nonlinear system becomes hybrid, since it has a mixed discrete/continuous dynamics. Under some assumptions, written in terms of Lyapunov functions, two event-based algorithms are suggested for nonlinear systems. The first algorithm is directly based on the variation of the Lyapunov functions. The last event-based algorithm is based on a selection of the input variables to be updated. The results are particularized to linear control systems and illustrated by numerical simulations of linear and nonlinear control systems