Approximation and Representation of Transfer Functions of MIMO Systems under Stability, Causality and Smoothness Constraints

The question whether or not there exists a (Schauder) basis in the space of all transfer functions for linear stable systems plays an important roll in system- and control theory because such a basis ensures the existents of stable filter banks. Using a deep result from mathematics, it is shown that there exists no uniformly bounded basis for stable linear systems, in general. Therefore, this paper restricts the set of all transfer functions by additional smoothness requirements and characterizes a large subspace of all causal and stable transfer function for which a Schauder basis exists