Alexandre Seuret, Christophe Prieur, Nicolas Marchand; Stability of non-linear systems by means of event-triggered sampling algorithms. IMA J Math Control Info 2014; 31 (3): 415-433. doi: 10.1093/imamci/dnt018
In this paper, the problem of feedback control implementation for non-linear 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 periodical 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 non-linear system becomes hybrid, since it has a mixed discrete and continuous dynamics. Under some assumptions, written in terms of Lyapunov functions, two event-based algorithms are suggested for non-linear 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 non-linear control systems.