Reachability of eigenspaces for interval circulant matrices in max-algebra

TL;DR

This paper investigates the reachability of eigenspaces in max-algebra for interval circulant matrices, classifying robustness types and exploring spectral properties and attraction cones within this mathematical framework.

Contribution

It introduces a classification of six types of interval robustness for circulant matrices in max-algebra and analyzes their spectral and eigenspace properties.

Findings

Classification of six robustness types for interval circulant matrices

Characterization of max-algebraic spectral properties of circulant matrices

Analysis of inclusion relations among attraction cones

Abstract

A nonnegative matrix A is said to be strongly robust if its max-algebraic eigencone is universally reachable, i.e., if the orbit of any initial vector ends up with a max-algebraic eigenvector of A. Consider the case when the initial vector is restricted to an interval and A can be any matrix from a given interval of nonnegative circulant matrices. The main aim of this paper is to classify and characterize the six types of interval robustness in this situation. This naturally leads us also to study the max-algebraic spectral theory of circulant matrices and the relation of inclusion between attraction cones of circulant matrices in max-algebra.