Exact controllability and spectrum assignment (Q1073740)

Let (A,B) be a linear system where the state operator A is a bounded linear operator on a Hilbert space \({\mathcal H}\) and the input operator B is a bounded linear operator from a Hilbert space \({\mathcal G}\) to \({\mathcal H}\). The system (A,B) is called exactly controllable if every vector of \({\mathcal H}\) belongs to the algebraic linear span of \(A^ kB({\mathcal G})\), \(k=0,1,2,... \). We give various conditions equivalent to exact controllability.