Quantized Periodic Event-triggered Control for LTI Systems with 1-bit Data Transmission

This paper presents a novel framework for periodic event-triggered control (PETC) coupled with dynamic quantization for linear systems. Unlike traditional time-driven control methods, our approach leverages event-based mechanisms to judiciously update control actions, thus minimizing computational load and network traffic. We introduce a two-level dynamic quantizer for encoding feedback information with a single bit, thereby enhancing resource efficiency. The proposed PETC mechanism decides the transmission instants based on the quantized output samples. The resulting system is modeled as a hybrid dynamical system to capture both continuous and discrete dynamics. Sufficient conditions for ensuring the stability of the closed-loop system are presented in the form of a linear matrix inequality. Through numerical simulations, we demonstrate that our approach captures the initial output within a finite time and significantly reduces data transmissions compared to traditional methods. This paper makes key contributions in the integration of dynamic quantization with PETC, leading to resource-efficient and stable control systems.