Pole-shifting for linear systems over commutative rings
The authors consider the problem of modifying by feedback the characteristic polynomial of a not necessarily reachable linear dynamical system over a commutative ring \(R\). They introduce the notion of PS ring in the same way as the notion of pole assignable ring is given for reachable systems. Then they prove that a bcs ring is a PS ring and that over a Prüfer domain these properties are equivalent. Finally, the authors study when the converse of the pole-shifting theorem is verified.
scientific article; zbMATH DE number 1758610