Internal positivity preserved model reduction

Jun E. Feng, James Lam, Zhan Shu, Qing Wang

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


This article studies model reduction of continuous-time stable positive linear systems under the Hankel norm, H norm and H2 norm performance. The reduced-order systems preserve the stability as well as the positivity of the original systems. This is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the Lyapunov matrices are decoupled with the system matrices. In this way, the positivity constraints in the reduced-order model can be imposed in a natural way. As the model reduction performances are expressed in linear matrix inequalities with equality constraints, the desired reduced-order positive models can be obtained by using the cone complementarity linearisation iterative algorithm. A numerical example is presented to illustrate the effectiveness of the given methods.

Original languageEnglish
Pages (from-to)575-584
Number of pages10
JournalInternational Journal of Control
Issue number3
Publication statusPublished - Mar 2010
Externally publishedYes


  • Cone complementarity linearisation
  • H norm
  • H norm
  • Hankel norm
  • Linear matrix inequality
  • Model reduction
  • Positive systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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