# On the Local Input-Output Stability of Event-Triggered Control Systems

## TL;DR

This paper introduces a new event-triggered control mechanism for nonlinear systems that maintains local L2 performance and extends inter-event times, improving efficiency while ensuring disturbance attenuation.

## Contribution

It proposes a novel triggering condition that preserves local L2 stability and analytically estimates increased inter-event periods for nonlinear control systems.

## Key findings

- Extended inter-event periods through the proposed triggering mechanism.
- Maintained local L2 disturbance attenuation in nonlinear systems.
- Validated results with illustrative examples.

## Abstract

This paper studies performance preserving event design in nonlinear event-based control systems based on a local L2-type performance criterion. Considering a finite gain local L2-stable disturbance driven continuous-time system, we propose a triggering mechanism so that the resulting sampled-data system preserves similar disturbance attenuation local L2-gain property. The results are applicable to nonlinear systems with exogenous disturbances bounded by some Lipschitz-continuous function of state. It is shown that an exponentially decaying function of time, combined with the proposed triggering condition, extends the inter-event periods. Compared to the existing works, this paper analytically estimates the increase in intersampling periods at least for an arbitrary period of time. We also propose a so-called discrete triggering condition to quantitatively find the improvement in inter-event times at least for an arbitrary number of triggering iterations. Illustrative examples support the analytically derived results.