Publication: Reachability of random Linear systems over finite fields
Reachability of random Linear systems over finite fields
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Helmke, U., Jordan, J., & Lieb, J. (2015). Reachability of random Linear systems over finite fields. In R. Pinto, P. R. Malonek, & P. Vettori (Eds.), Coding Theory and Applications (pp. 217–225). https://doi.org/10.1007/978-3-319-17296-5_23
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This paper deals with the probability of classical system-theoretic properties of random linear systems defined over a finite field. Explicit formulas are derived for the probability that the reachability matrix of a linear system has rank r. We also calculate the probability that the parallel connection of two single-input systems is reachable. Our results should be viewed as a first step to calculate the probability that a network of linear systems is reachable.
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Helmke, U., Jordan, J., & Lieb, J. (2015). Reachability of random Linear systems over finite fields. In R. Pinto, P. R. Malonek, & P. Vettori (Eds.), Coding Theory and Applications (pp. 217–225). https://doi.org/10.1007/978-3-319-17296-5_23