Minimal positive realizations of transfer functions with nonnegative multiple poles

Béla Nagy, Máté Matolcsi

Research output: Contribution to journalArticle

29 Citations (Scopus)


This note concerns a particular case of the minimality problem in positive system theory. A standard result in linear system theory states that any nth-order rational transfer function of a discrete time-invariant linear single-input-single-output (SISO) system admits a realization of order n. In some applications, however, one is restricted to realizations with nonnegative entries (i.e., a positive system), and it is known that this restriction may force the order N of realizations to be strictly larger than n. A general solution to the minimality problem (i.e., determining the smallest possible value of N) is not known. In this note, we consider the case of transfer functions with nonnegative multiple poles, and give sufficient conditions for the existence of positive realizations of order N = n. With the help of our results we also give an improvement of an existing result in positive system theory.

Original languageEnglish
Pages (from-to)1447-1450
Number of pages4
JournalIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - Sep 1 2005


  • Discrete-time filtering
  • Minimal realizations
  • Positive linear systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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