A tropical geometry approach to BIBO stability

TL;DR

This paper introduces a tropical geometry-based method to determine BIBO stability of multi linear time invariant systems using amoebas of Laurent polynomials, providing simple criteria and an algorithmic approach.

Contribution

It establishes a novel connection between tropical geometry and control theory, offering new criteria and algorithms for BIBO stability analysis.

Findings

Criteria for BIBO stability based on amoeba geometry

Algorithmic procedure for stability testing

Relation between amoeba position and system stability

Abstract

Given a Laurent polynomial F and its amoeba AF. We relate here the question of the BIBO stability of a multi linear time invariant system with a rational transfer function. We formulate very simple criteria for BIBO strong or weak stability in terms of the position of the origin 0 with respect to the amoeba AF and suggest an algorithmic procedure in order to test such property.