Random matrices and controllability of dynamical systems

TL;DR

This paper introduces the concept of epsilon-uncontrollability for random linear systems and provides estimates for Gaussian orthogonal ensemble matrices, combining systems theory, probability, and convex geometry tools.

Contribution

It defines epsilon-uncontrollability for random systems and offers probabilistic estimates specifically for Gaussian orthogonal ensemble matrices.

Findings

Defined epsilon-uncontrollability for random systems

Provided estimates for Gaussian orthogonal ensemble matrices

Utilized interdisciplinary mathematical tools

Abstract

We introduce the concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the $\epsilon$-uncontrollability in the case where the matrices come from the Gaussian orthogonal ensemble. Our proof utilizes tools from systems theory, probability theory and convex geometry.