On the absence of limit cycles in state-space digital filters with minimum L2-sensitivity

Shunsuke Yamaki, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


This brief proposes a systematic approach to synthesis of limit cycle free state-space digital filters with minimum L2-sensitivity. We synthesize the minimum L2-sensitivity realization adopting the balanced realization as an initial realization. The coordinate transformation matrix which transforms the balanced realization into the minimum L2-sensitivity realization is expressed as the product of a positive definite symmetric matrix and arbitrary orthogonal matrix. We show that the controllability and observability Gramians of the minimum L2-sensitivity realization satisfy a sufficient condition for the absence of limit cycles when we select an appropriate orthogonal matrix. As a result, the minimum L2-sensitivity realization without limit cycles can be synthesized by selecting an appropriate orthogonal matrix.

Original languageEnglish
Pages (from-to)46-50
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number1
Publication statusPublished - 2008
Externally publishedYes


  • Controllability Gramian
  • Limit cycles
  • Minimum L-sensitivity realization
  • Observability Gramian
  • State-space digital filters

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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