Analysis of second-order modes of linear discrete-time systems under bounded-real transformations

Shunsuke Koshita, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless boundedreal transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.

Original languageEnglish
Pages (from-to)2510-2515
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number11
Publication statusPublished - 2007 Nov


  • Bounded-real transformation
  • Controllability gramian
  • Discrete-time bounded-real lemma
  • Discrete-time state-space system
  • 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


Dive into the research topics of 'Analysis of second-order modes of linear discrete-time systems under bounded-real transformations'. Together they form a unique fingerprint.

Cite this