Classification of control operators for a class of distributed delayed systems with application of diffusion case

Abstract

his work investigates the classification of spatio-temporal (distributed parameter) systems, with
a focus on the concept of domination in a class of delayed distributed systems. We examine the possibility
of classifying such systems based on the structure of input and output operators, even when the underlying
dynamics differ. Precise definitions of weak and exact domination are proposed, along with key properties and
characterization results for general controlled systems and associated input operators. The analysis extends to
the case of multi-actuator and multi-sensor configurations.Applications to parabolic systems are provided to
illustrate the theoretical results. Furthermore, the relationship between domination and the problem of exact
reachability with minimum energy is explored.