A New Lyapunov-Based Event-Triggered Control of Linear Systems

This article introduces a new Lyapunov sampling for event-triggered linear systems. Contrary to the majority of the existing literature, our proposed event-triggering mechanism (ETM) directly deals with the Lyapunov derivative rather than its upper bounds. Moreover, a new concept of ideality is introduced, which serves as a measure of conservativity of the triggering mechanism during the stability regions of trajectories. To construct the ETM, we employ a diagonal transformation to facilitate the design in a component-wise fashion. Moreover, the interpretation of stating ETM in the transformed coordinate is given by when the trajectories reach
$p$
-norm contour curves. A proof of Zeno behavior exclusion is also given, which is required to justify the efficiency of the presented method for practical implementation. The approach is illustrated by a compelling example.