The Generic Degree of Autonomy

Abstract

This paper calculates the degree of autonomy of a generic autonomous n-D system given by the kernel of a partial difference operator. The calculation implies that attaching a generic controller to a non-autonomous 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 an open (dense) subset of the set of all n-D systems with the Zariski topology.

This arxiv version corrects errors in the published version of the paper (SIAM Journal on Applied Algebra Geometry, 2(3), 410-427, 2018), where an error in Theorem 3.1 propagated to the statements of Theorems 3.2, 4.1 and 4.2. These corrections will also appear as a Corrigendum