Name
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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.3934/amc.2016.10.63 | ADVANCES IN MATHEMATICS OF COMMUNICATIONS |
Keywords | Field | DocType |
Linear systems,finite fields,reachability,Grassmann manifolds,parallel connection | Discrete mathematics,Combinatorics,Finite field,Linear system,Matrix (mathematics),Reachability matrix,Reachability,Mathematics | Journal |
Volume | Issue | ISSN |
10 | SP1 | 1930-5346 |
Citations | PageRank | References |
2 | 0.48 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Uwe Helmke | 1 | 337 | 42.53 |
| Jordan, J. | 2 | 14 | 1.85 |
| Julia Lieb | 3 | 2 | 1.50 |