Regular implementability and its application to stabilization of system behaviors

We study control by interconnection of linear differential systems. We give necessary and sufficient conditions for regular implementability of a given linear differential system. We formulate the problems of stabilization and pole placement as problems of finding suitable, regularly implementable sub-behaviors of the manifest plant behavior. The problem formulations and their resolutions are completely representation free, and specified in terms of the system dynamics only. Control is viewed as regular interconnection. A controller is a system that constrains the plant behavior through a distinguished set of variables, namely, the control variables. The issue of implementation of a controller in the feedback configuration and its relation to regularity of interconnection is addressed. Freedom of disturbances in a plant and regular interconnection with a controller also turn out to be inter-related.