Analysis of Information Theoretic Limitation for Linear Time Invariant Feedback Systems

TL;DR

This paper introduces a new fundamental inequality in feedback control systems that links information theory and control theory, extending previous results and providing deeper insights into system limitations.

Contribution

A novel Bode-like inequality connecting directed information, mutual information, and sensitivity functions in causal feedback systems is proposed.

Findings

The inequality generalizes existing feedback system results.

It relates information measures to control system sensitivity.

Provides a new theoretical framework for feedback system limitations.

Abstract

Information-theoretic fundamental limitation in feedback control system is an important topic for decades. In this paper, a new bode-like fundamental inequality in causal feedback control system is developed. This inequality relates directed information, mutual information and bode sensitivity functions. This inequality recovers previous known results in feedback system as special cases.