Classification of spatio-temporal systems: Concept of domination

Abstract

This work is an overview on spatio-temporal (distributed) systems classification. More precisely, it concerns the notion of domination for a class of distributed parameter systems. We explore the possibility of classification of such systems based on the choice of input and output operators. The systems to be compared may have different dynamics. We give appropriate definitions of the weak and exact domination, the main properties and characterization results for general controlled systems and input operators. By duality, similar results are deduced for observed systems and output operators. The cases of multi-actuators and multi-sensors are considered. Relationship with the notion of remediability is also explored. Applications of the results to the case of parabolic and hyperbolic systems are considered.