Zero-Error Feedback Capacity for Bounded Stabilization and Finite-State Additive Noise Channels

TL;DR

This paper introduces a new concept of uniform zero-error feedback capacity for channels with memory and derives conditions for stabilizing unstable linear systems over such channels without channel state information.

Contribution

It extends classical zero-error feedback capacity to channels with memory and links it to stabilization of linear systems without channel state information.

Findings

Defined uniform zero-error feedback capacity $ C_{0f} $ for channels with memory.

Derived a tight condition for bounded stabilization of unstable linear systems.

Established the relationship between feedback capacity and control stability.

Abstract

This article studies the zero-error feedback capacity of {\em causal} discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of {\em uniform zero-error feedback capacity} $ C_{0f} $ for such channels is introduced. Using this notion a tight condition for {bounded} stabilization of unstable {noisy} linear systems via causal channels is obtained, assuming no {channel} state information at either end of the channel.