Stabilization of uncertain systems using quantized and lossy observations and uncertain control inputs

TL;DR

This paper addresses the stabilization of uncertain networked control systems with quantized and lossy observations, deriving conditions for mean square stability and demonstrating the effectiveness of nonuniform quantizers in reducing data rate requirements.

Contribution

It introduces stability conditions for uncertain systems under quantization and packet loss, highlighting the advantages of nonuniform quantizers over uniform ones.

Findings

Nonuniform quantizers can achieve stability at lower data rates.

Derived conditions relate data rate, packet loss, and uncertainty for stability.

Stability is characterized in terms of mean square stability under network constraints.

Abstract

In this paper, we consider a stabilization problem of an uncertain system in a networked control setting. Due to the network, the measurements are quantized to finite-bit signals and may be randomly lost in the communication. We study uncertain autoregressive systems whose state and input parameters vary within given intervals. We derive conditions for making the plant output to be mean square stable, characterizing limitations on data rate, packet loss probabilities, and magnitudes of uncertainty. It is shown that a specific class of nonuniform quantizers can achieve stability with a lower data rate compared with the common uniform one.