TY - GEN

T1 - Approximation and representation of transfer functions of MIMO systems under stability, causality and smoothness constraints

AU - Boche, Holger

AU - Pohl, Volker

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33749616024&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33749616024

SN - 0780394577

SN - 9780780394575

T3 - Proceedings of the Annual Southeastern Symposium on System Theory

SP - 128

EP - 132

BT - Proceedings of the 38th Southeastern Symposium on System Theory

T2 - 38th Southeastern Symposium on System Theory

Y2 - 5 March 2006 through 7 March 2006

ER -