Self-triggered Stabilization of Discrete-time Linear Systems with Quantized State Measurements

TL;DR

This paper proposes a joint design method for encoding and self-triggering mechanisms to stabilize discrete-time linear systems with quantized measurements over finite data-rate channels, ensuring robustness against quantization errors.

Contribution

It introduces a novel joint design approach combining encoding schemes with self-triggered control to achieve stabilization despite quantization and data-rate limitations.

Findings

Effective stabilization with quantized data

Robustness to quantization errors demonstrated

Joint encoding and triggering improves control performance

Abstract

We study the self-triggered stabilization of discrete-time linear systems with quantized state measurements. In the networked control system we consider, sensors may be spatially distributed and be connected to a self-triggering mechanism through finite data-rate channels. Each sensor independently encodes its measurements and sends them to the self-triggering mechanism. The self-triggering mechanism integrates quantized measurement data and then computes sampling times. Assuming that the closed-loop system is stable in the absence of quantization and self-triggered sampling, we propose a joint design method of an encoding scheme and a self-triggering mechanism for stabilization. To deal with data inaccuracy due to quantization, the proposed self-triggering mechanism uses not only quantized data but also an upper bound of quantization errors, which is shared with a decoder.