Publication: Probability estimates for reachability of linear systems defined over finite fields
Probability estimates for reachability of linear systems defined over finite fields
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Lieb, J., Jordan, J., & Helmke, U. (2016). Probability estimates for reachability of linear systems defined over finite fields. Advances in Mathematics of Communication, 10(1), 63–78. https://doi.org/10.3934/amc.2016.10.63
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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 syste
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- Lieb, Julia
- Jordan, Jens
- Helmke, Uwe
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Lieb, J., Jordan, J., & Helmke, U. (2016). Probability estimates for reachability of linear systems defined over finite fields. Advances in Mathematics of Communication, 10(1), 63–78. https://doi.org/10.3934/amc.2016.10.63
