Some criteria for spectral finiteness of a finite subset of the real matrix space $\mathbb{R}^{d\times d}$

TL;DR

This paper introduces practical criteria to determine whether a finite set of real matrices has a finite spectral radius, aiding in stability analysis and control theory applications.

Contribution

It provides new checkable conditions for spectral finiteness of finite matrix sets, advancing the theoretical tools available for matrix analysis.

Findings

Derived checkable criteria for spectral finiteness

Applicable to matrices in real space of dimension d

Facilitates stability analysis in control systems

Abstract

In this paper, we present some checkable criteria for the spectral finiteness of a finite subset of the real $d\times d$ matrix space $\mathbb{R}^{d\times d}$, where $2\le d<\infty$.