Open AccessRandom matrices and controllability of dynamical systems
Author(s) -
John Leventides,
Nick Poulios,
Costas Poulios
Publication year - 2021
Publication title -
ima journal of mathematical control and information
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.385
H-Index - 37
eISSN - 1471-6887
pISSN - 0265-0754
DOI - 10.1093/imamci/dnab011
Subject(s) - random matrix , controllability , linear system , gaussian , mathematics , dynamical systems theory , regular polygon , systems theory , linear dynamical system , pure mathematics , algebra over a field , computer science , mathematical analysis , geometry , physics , quantum mechanics , eigenvalues and eigenvectors , artificial intelligence
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concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices.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.
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