Module theoretic approach to controllability of convolutional systems

Both the behavioral approach proposed by Willems and the module theoretic approach proposed by Fliess provide a representation free theory of dynamical systems. According to these approaches, controllability is an intrinsic system property independent of the system representation. In the first part of this paper a comparison between the behavioral approach and the module theoretic approach to convolutional systems is proposed. Then, controllability of this class of systems is analyzed according to these two approaches. This concept is related to the existence of image representations. Finally, the same analysis is proposed for systems described by delay-differential equations.