A lowerbound on the dimension of positive realizations

Author

Nagy, Béla ; Matolcsi, Máté

Author_Institution

Math. Dept., Tech. Univ., Budapest, Hungary

Volume

50

Issue

6

fYear

2003

fDate

6/1/2003 12:00:00 AM

Firstpage

782

Lastpage

784

Abstract

A basic phenomenon in positive system theory is that the dimension N of an arbitrary positive realization of a given transfer function H(z) may be strictly larger than the dimension n of its minimal realizations. The aim of this brief is to provide a nontrivial lowerbound on the value of N under the assumption that there exists a time instant k₀ at which the (always nonnegative) impulse response of H(z) is 0 but the impulse response becomes strictly positive for all k>k₀. Transfer functions with this property may be regarded as extremal cases in positive system theory.

Keywords

directed graphs; discrete time systems; linear systems; realisation theory; transfer functions; transient response; arbitrary positive realization; digraph terminology; dimension estimates; discrete time-invariant linear scalar system; extremal cases; impulse response; nontrivial lowerbound; positive system theory; time instant; transfer function; Circuits; Controllability; Equations; Linear systems; Mathematics; Time factors; Transfer functions;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/TCSI.2003.812609

Filename

1208622