Tracking and regulation in the behavioral framework

This paper considers the problem of tracking and regulation for the class of linear differential systems in the behavioral framework. Given a plant, together with an exosystem generating the disturbances and the reference signals, the problem of tracking and regulation is to find a controller such that the plant variable tracks the reference signal regardless of the disturbance acting on the system. A controller which achieves this design objective is called a regulator for the plant with respect to the exosystem. In this paper we formulate the tracking and regulation problem in the behavioral framework, with control as interconnection. We obtain necessary and sufficient conditions for the existence of a controller which acts like a regulator for the plant with respect to the exosystem. The problem formulation and its resolution are completely representation free, and specified only in terms of the plant and the exosystem dynamics.