In this paper, positive-real systems under lossless positive-real transformations are investigated. Let G(s) be the transfer function matrix of a continuous-time positive-real system of order n and F(s) a lossless transfer function of order nF. We prove here that the lossless positive-real transformed system, i.e. G(F(s)), is also positive-real. Furthermore, the stochastic balanced representation of positive-real systems under lossless positive-real transformations is considered. In particular, it is proved that the positive-real characteristic values πj of G(F(s)) are the same of G(s) each with multiplicity nF, independently from the choice of F(s). This property is exploited in the design of reduced order models based on stochastic balancing. Finally, the proposed technique is a passivity preserving model order reduction method, since it is proven that the reduced order model of G(F(s)) is still positive-real. An error bound for truncation related to the invariants πj is also derived.

Positive-real systems under lossless transformations: Invariants and reduced order models

BUSCARINO, Arturo;FORTUNA, Luigi;FRASCA, MATTIA;
2017-01-01

Abstract

In this paper, positive-real systems under lossless positive-real transformations are investigated. Let G(s) be the transfer function matrix of a continuous-time positive-real system of order n and F(s) a lossless transfer function of order nF. We prove here that the lossless positive-real transformed system, i.e. G(F(s)), is also positive-real. Furthermore, the stochastic balanced representation of positive-real systems under lossless positive-real transformations is considered. In particular, it is proved that the positive-real characteristic values πj of G(F(s)) are the same of G(s) each with multiplicity nF, independently from the choice of F(s). This property is exploited in the design of reduced order models based on stochastic balancing. Finally, the proposed technique is a passivity preserving model order reduction method, since it is proven that the reduced order model of G(F(s)) is still positive-real. An error bound for truncation related to the invariants πj is also derived.
2017
Control and Systems Engineering; Signal Processing; Computer Networks and Communications; Applied Mathematics
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0016003217301825-Positive-real systems under lossless transformations.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Dimensione 704.08 kB
Formato Adobe PDF
704.08 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/300093
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact