System theory for system identification

Prediction and control problems require for their solution mathematical models in the form of dynamic systems. In system theory the approach to this problem is to investigate realization problems for system identification. Novel in this paper is the emphasis on the realization problem for observation-based realizations and on the realization problem for control. A major aspect of these realization problems is computation and complexity. Algebraic approaches to realization problems may lead to the distinction of subclasses of systems with required finiteness properties, to decompositions, and to abstractions for hierarchical systems.