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This article proposes a general framework for analyzing continuous‐time systems controlled by event‐triggered algorithms. Closed‐loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event‐triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions. Using recently developed tools for robust stability, properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated by several event‐triggered strategies available in the literature, and observations about their key dynamical properties are made.

In this paper, we define solutions for hybrid systems with prespecified hybrid inputs. Unlike previous work where solutions and inputs are assumed to be defined on the same domain a priori, we consider the case where intervals of flow and jump times of the input are not necessarily synchronized with those of the state trajectory. This happens in particular when the input is the output of another hybrid system, for instance, in the context of observer design or reference tracking. The proposed approach relies on reparametrizing the jumps of the input in order to write it on a common domain. The solutions then consist of a pair made of the state trajectory and the reparametrized input. Our definition generalizes the notions of solutions of continuous‐time and discrete‐time systems with inputs. We provide an algorithm that automatically performs the construction of solutions for a given hybrid input. In the context of hybrid interconnections, we show how the solutions of the individual systems can be linked to the solutions of a closed‐loop system. Example illustrate the notions and the proposed algorithm.