The Generic Degree of Autonomy

Abstract

This paper calculates the degree of autonomy of a generic autonomous $n-D$ system defined by the kernel of a partial difference operator. The calculation implies that attaching a generic controller to a nonautonomous system, results in a controlled system whose degree of autonomy is the maximum possible. Thus a generic controller is maximally efficient with respect to the criterion of maximising degree of autonomy. The term generic here refers to a dense open subset of the set of all $n-D$ systems with the Zariski topology.