Stabilization of infinite-dimensional systems under quantization and packet loss

TL;DR

This paper presents a method for stabilizing infinite-dimensional systems with quantization and packet loss, ensuring exponential convergence under certain bounds and providing techniques to compute operator norms.

Contribution

It introduces a novel design method for dynamic quantizers with zoom parameters tailored for infinite-dimensional systems under packet loss.

Findings

Closed-loop state exponentially converges to zero under specified bounds.

Proposed quantizer design accounts for packet loss and quantization errors.

Methods for approximating operator norms of system dynamics.

Abstract

We study the problem of stabilizing infinite-dimensional systems with input and output quantization. The closed-loop system we consider is subject to packet loss, whose average duration is assumed to be bounded. Given a bound on the initial state, we propose a design method for dynamic quantizers with zoom parameters. We show that the closed-loop state starting in a given region exponentially converges to zero if bounds on quantization errors and packet-loss intervals satisfy suitable conditions. Since the norms of the operators representing the system dynamics are used in the proposed quantizer design, we also present methods for approximately computing the operator norms.