An abstract Nyquist criterion containing old and new results

TL;DR

This paper develops a general abstract Nyquist criterion that unifies and extends existing results, providing a comprehensive framework applicable to various control system stability analyses.

Contribution

It introduces a broad, abstract formulation of the Nyquist criterion that encompasses both classical and novel versions, enhancing theoretical understanding.

Findings

Recovering classical Nyquist criteria

Deriving new versions of the Nyquist criterion

Providing a unified theoretical framework

Abstract

We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.