Abstract
This work concerns the analysis of a class of linear dynamical systems. We study the possibility of comparing input operators, with respect to the output one, and we give characterization results. Various situations are examined, applications and illustrative examples are presented. Under convenient hypothesis, we also show how to find the optimal control ensuring the compensation of a disturbance in the finite time or asymptotic cases. The relationship with the notions of controllabi-lity, stability and stabilizability is examined. Here also, applications and examples illustrating different results and situations are given.