Sign Stability via Root Locus Analysis

TL;DR

This paper uses root locus analysis to clarify the necessary conditions for sign stability in systems, aiding understanding of qualitative stability based solely on parameter signs.

Contribution

It introduces a novel application of root locus analysis to elucidate the conditions for structural stability in systems based on parameter signs.

Findings

Root locus analysis reveals key conditions for sign stability.

Necessary conditions for qualitative stability are illustrated.

Method enhances understanding of stability without exact parameter values.

Abstract

With the rise of network science old topics in ecology and economics are resurfacing. One such topic is structural stability (often referred to as qualitative stability or sign stability). A system is deemed structurally stable if the system remains stable for all possible parameter variations so long as the parameters do not change sign. This type of stability analysis is appealing when studying real systems as the underlying stability result only requires the scientist or engineer to know the sign of the parameters in the model and not the specific values. The necessary and sufficient conditions for qualitative stability however are opaque. In order to shed light on those conditions root locus analysis is employed. This technique allows us to illustrate the necessary conditions for qualitative stability.