Input and output parameters domination in infinite dimensional systems

This work concerns the systems analysis of a class of distributed parameter systems, and more precisely the notions of weak and exact domination. We introduce and we study these concepts for controlled and observed systems. This consists to study the possibility of comparison of systems and input-output parameters. We give the main characterization results and properties of the notion of domination for control operators and then for observation operators. We show that there is a duality between these two cases. We also examine the case of actuators and sensors. Various other situations and extensions are considered, applications are also given. The relationship between the domination and other concepts as controllability, observability and compensation are examined.