An $\mathcal{L}_{\mathrm{p}}$ -norm framework for event-triggered control
This paper presents a novel event-triggered control (ETC) design framework based on measured $\mathcal{L}_{p}$ norms. We consider a class of systems with finite $\mathcal{L}_{p}$ gain from the network-induced error to a chosen output. The $\mathcal{L}_{p}$ norms of the network-induced error and the chosen output since the last sampling time are used to formulate a class of triggering rules. Based on a small-gain condition, we derive an explicit expression for the $\mathcal{L}_{p}$ gain of the resulting closed-loop systems and present a time-regularization, which can be used to guarantee a lower bound on the inter-sampling times. The proposed framework is based on a different stability- and triggering concept compared to ETC approaches from the literature, and thus may yield new types of dynamical properties for the closed-loop system. However, for specific output choices it can lead to similar triggering rules as “standard” static and dynamic ETC approaches based on input-to-state stability and yields therefore a novel interpretation for some of the existing triggering rules. We illustrate the proposed framework with a numerical example from the literature.