Controllability in infinite-dimensional Hilbert spaces (Q5956096)

Using some results from set-valued analysis, the author exhibits a necessary and sufficient condition for controllability in infinite-dimensional Hilbert spaces of the system NEWLINE\[NEWLINEx'(t)=A(t)x(t)+B(t,u(t)), \quad t\in T:=[0,a],NEWLINE\]NEWLINE where \(A(t), t\in T\), is a family of linear and densely defined operators generating an evolution operator \(B: T\times Y\to H\) and \(Y\) respectively \(H\) is a separable Banach respectively Hilbert space. Under some circumstances, this condition reduces to the Kalman criterion.