Realization of certain input-output correspondences in a finite- dimensional space (Q810429)

Let A be a maximal monotone operator acting from a Hilbert space H to the subsets of H. The author considers a control system described by \(\dot x(t)+Ax(t)=\dot u(t),\) \(x(t_ 0)=x_ 0\). Parallely, he defines an ``input-output transformer'' possessing the standard properties of a semigroup generated by a differential equation. Three realization theorems are proved extending the known Crandall-Pazy result on representation of contracting continuous semigroups by maximal monotone operators.