Invariance of second-order modes of linear continuous-time systems under typical frequency transformations

Masayuki Kawamata, Yousuke Mizukami, Shunsuke Koshita

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpasshighpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.

Original languageEnglish
Pages (from-to)1481-1486
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE90-A
Issue number7
DOIs
Publication statusPublished - 2007 Jul

Keywords

  • Continuous-time state-space system
  • Controllability Gramian
  • Frequency transformation
  • Invariance
  • Observability Gramian
  • Second-order mode (Hankel singular value)

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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