Carathéodory-Pesin structures associated with control systems

We introduce five Carathéodory-Pesin (C-P) structures for control systems and show that the invariance entropy studied by Colonius and Kawan (2009) and the topological feedback entropy in Colonius et al., (2013) are just quantities generated by some special C-P structures that give the characteristics of dimension types for these classical control entropies. We explore some basic properties of these control entropies and investigate the relationships among these quantities. In addition, we also obtain a sufficient condition for the existence of a generator for the invariance entropy, which was posed by Kawan (2013, p. 87) as an open question.