Foundations of system theory: The hankel matrix

摘要

After introducing the notion of “dynamical interpretation functor” to provide a general methodology for nonlinear state-space description, we define the Hankel matrix for an arbitrary adjoint system. This returns the usual definition for linear systems, but also applies to sequential machines, group machines, and bilinear machines. We provide row-recurrence and column-recurrence criteria for the “finite-dimensional” realizability of a Hankel matrix. Finally, we introduce the concept of subquotient ascendancy to define an absolute notion of finite rank in terms of which we analyze partial realizations of Hankel matrices.