On generic reachability over certain Banach algebras (Q1115378)

It is shown that reachability is weakly generic over commutative Banach algebras with dense set of units in the sense that the set of pairs of matrices over \({\mathcal A}\) whose reachability matrix is right invertible is open and dense. \(\ell^ 1({\mathbb{Z}},{\mathbb{R}})\) turns out to be an example. Furthermore the reachability of a pair of matrices is seen to be equivalent to almost state reachability of the corresponding continuous- time autonomous system in the case where \({\mathcal A}\) contains units.