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Probability estimates for reachability of linear systems defined over finite fields


Lieb, Julia; Jordan, Jens; Helmke, Uwe (2016). Probability estimates for reachability of linear systems defined over finite fields. Advances in Mathematics of Communication, 10(1):63-78.

Abstract

This paper deals with the probability that random linear systems defined over a finite field are reachable. Explicit formulas are derived for the probabilities that a linear input-state system is reachable, that the reachability matrix has a prescribed rank, as well as for the number of cyclic vectors of a cyclic matrix. We also estimate the probability that the parallel connection of finitely many single-input systems is reachable. These results may be viewed as a first step to calculate the probability that a network of linear systems is reachable.

Abstract

This paper deals with the probability that random linear systems defined over a finite field are reachable. Explicit formulas are derived for the probabilities that a linear input-state system is reachable, that the reachability matrix has a prescribed rank, as well as for the number of cyclic vectors of a cyclic matrix. We also estimate the probability that the parallel connection of finitely many single-input systems is reachable. These results may be viewed as a first step to calculate the probability that a network of linear systems is reachable.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Physical Sciences > Computer Networks and Communications
Physical Sciences > Discrete Mathematics and Combinatorics
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:General Medicine
Language:English
Date:1 March 2016
Deposited On:10 Nov 2021 15:32
Last Modified:26 Apr 2024 01:36
Publisher:American Institute of Mathematical Sciences (A I M S Press)
ISSN:1930-5338
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.3934/amc.2016.10.63
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)