The notion of almost zeros and randomness-Reference-Cited by-同舟云学术

The notion of almost zeros and randomness

Published:2021-04-22 Issue: Volume: Page:
ISSN:0265-0754
Container-title:IMA Journal of Mathematical Control and Information
language:en
Short-container-title:

Author:

Leventides J¹,Karcanias N²,Poulios N C¹

Affiliation:

1. Department of Economics, Division of Mathematics, Informatics and Quantitative Methods, National and Kapodistrian University of Athens (NKUA), 1, Sofokleous str, 4th floor, P.O. 10559, Greece

2. Systems and Control Engineering Centre, Department of Engineering, School of Mathematics, Computer Science and Engineering, City University of London, Northampton Square, London EC1V 0HB, UK

Abstract

Abstract We investigate the problem of almost zeros of polynomial matrices as used in system theory. It is related to the controllability and observability notion of systems as well as the determination of Macmillan degree and complexity of systems. We also present some new results on this important invariant in the light of randomness and we prove an uncertainty type relation appearing in such ensembles of operators.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Control and Optimization,Control and Systems Engineering

Link

https://academic.oup.com/imamci/advance-article-pdf/doi/10.1093/imamci/dnab008/41161283/dnab008.pdf

Reference10 articles.

1. Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation;Fatouros;Comput. Math. Appl.

2. Grassmann invariants, almost zeros and the determinantal zero, pole assignment problems of linear multivariable systems;Giannakopoulos;Int. J. Control

3. Necessary and sufficient conditions for zero assignment by constant squaring down;Giannakopoulos;Linear Algebra Appl.,1989

4. Almost zeros of a set of polynomials;Giannakopoulos;Internat. J. Control

5. Nearest common root of polynomials, approximate greatest common divisor and the structured singular value;Halikias;IMA J. Math. Control Inform