Passivity and Finite-Gain Performance for Two-Dimensional Digital Filters: The FM LSS Model Case

Choon Ki Ahn, Haranath Kar

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)


This brief considers the two-dimensional (2-D) passivity performance analysis problem of 2-D digital filters in the Fornasini-Marchesini local state-space (FM LSS) form. The purpose is to establish a new criterion in terms of linear matrix inequality such that the 2-D digital filters in the FM LSS form ensure 2-D passivity performance with a storage function. Moreover, this brief reveals that the 2-D digital filters exhibit the 2-D finite-gain performance under the proposed criterion. Without interference, the criterion guarantees the asymptotic stability of 2-D digital filters. An application example to a 2-D low-pass filter is given to demonstrate the usefulness of the presented passivity criterion. The criteria in this brief and in a previous work of one of the authors, as a whole, give methodical results for the 2-D passive removal of the overflow oscillation of 2-D digital filters with external inferences.

Original languageEnglish
Article number7111232
Pages (from-to)871-875
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number9
Publication statusPublished - 2015 Sept 1

Bibliographical note

Publisher Copyright:
© 2004-2012 IEEE.


  • Fornasini-Marchesini local state-space (FM LSS) model
  • Passivity
  • linear matrix inequality (LMI)
  • two-dimensional (2-D) digital filter

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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