Random matrices and controllability of dynamical systems

2020/11/23 by John Leventides, Leventides, John, Nick Poulios +3
Mathematics · #37H99 #37N35 #60B20 #93B05 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37H99 #msc:37N35 #msc:60B20 #msc:93B05

paper · pdf · doi:10.48550/arxiv.2011.11147

arxiv created 2020/11/23 · arxiv updated 2020/11/24

Abstract

We introduce the concept of ε-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the ε-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.

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