# Decentralized Periodic Event-Triggered Control with Quantization and Asynchronous Communication

## TL;DR

This paper introduces ADPETC, an extension of ADETC that incorporates periodic sampling and studies its stability and L2-gain properties in the presence of disturbances, suitable for wireless networked control systems.

## Contribution

The paper extends ADETC by integrating periodic sampling into the decentralized event-triggered control framework and analyzes its stability and disturbance rejection capabilities.

## Key findings

- ADPETC maintains stability under disturbances.
- The approach reduces communication load in wireless networks.
- Numerical example validates theoretical results.

## Abstract

Asynchronous decentralized event-triggered control (ADETC) is an implementation of controllers characterized by decentralized event generation, asynchronous sampling updates, and dynamic quantization. Combining those elements in ADETC results in a parsimonious transmission of information which makes it suitable for wireless networked implementations. We extend the previous work on ADETC by introducing periodic sampling, denoting our proposal asynchronous decentralized periodic event-triggered control (ADPETC), and study the stability and L2-gain of ADPETC for implementations affected by disturbances. In ADPETC, at each sampling time, quantized measurements from those sensors that triggered a local event are transmitted to a dynamic controller that computes control actions; the quantized control actions are then transmitted to the corresponding actuators only if certain events are also triggered for the corresponding actuator. The developed theory is demonstrated and illustrated via a numerical example.