Novel Results on Generalized Dissipativity of Two-Dimensional Digital Filters

Choon Ki Ahn, Peng Shi, Hamid Reza Karimi

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

Existing results on the generalized dissipativity of digital filters are limited to 1-D cases. This brief presents some novel results on the generalized dissipativity of 2-D filters in the discrete Fornasini-Marchesini second (FMS) form. More specifically, we propose a criterion to ascertain that single 2-D filters in the discrete FMS form are 2-D generalized dissipative. Using this result, a condition is established such that the interconnected 2-D filters in the discrete FMS form are 2-D generalized dissipative. Furthermore, the asymptotic stability of unforced interconnected 2-D filters is examined. It is shown that the results developed in our recent work for 1-D filters and in this brief for 2-D filters serve as an overall framework for the generalized dissipativity of digital filters.

Original languageEnglish
Article number7419904
Pages (from-to)893-897
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Volume63
Issue number9
DOIs
Publication statusPublished - 2016 Sep 1

Fingerprint

Digital filters
Asymptotic stability

Keywords

  • 2-D filter
  • Fornasini-Marchesini second (FMS) form
  • generalized dissipativity
  • interconnected filter

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Novel Results on Generalized Dissipativity of Two-Dimensional Digital Filters. / Ahn, Choon Ki; Shi, Peng; Karimi, Hamid Reza.

In: IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 63, No. 9, 7419904, 01.09.2016, p. 893-897.

Research output: Contribution to journalArticle

@article{a729b446a4c3483eba59420e734842fb,
title = "Novel Results on Generalized Dissipativity of Two-Dimensional Digital Filters",
abstract = "Existing results on the generalized dissipativity of digital filters are limited to 1-D cases. This brief presents some novel results on the generalized dissipativity of 2-D filters in the discrete Fornasini-Marchesini second (FMS) form. More specifically, we propose a criterion to ascertain that single 2-D filters in the discrete FMS form are 2-D generalized dissipative. Using this result, a condition is established such that the interconnected 2-D filters in the discrete FMS form are 2-D generalized dissipative. Furthermore, the asymptotic stability of unforced interconnected 2-D filters is examined. It is shown that the results developed in our recent work for 1-D filters and in this brief for 2-D filters serve as an overall framework for the generalized dissipativity of digital filters.",
keywords = "2-D filter, Fornasini-Marchesini second (FMS) form, generalized dissipativity, interconnected filter",
author = "Ahn, {Choon Ki} and Peng Shi and Karimi, {Hamid Reza}",
year = "2016",
month = "9",
day = "1",
doi = "10.1109/TCSII.2016.2535039",
language = "English",
volume = "63",
pages = "893--897",
journal = "IEEE Transactions on Circuits and Systems I: Regular Papers",
issn = "1549-8328",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "9",

}

TY - JOUR

T1 - Novel Results on Generalized Dissipativity of Two-Dimensional Digital Filters

AU - Ahn, Choon Ki

AU - Shi, Peng

AU - Karimi, Hamid Reza

PY - 2016/9/1

Y1 - 2016/9/1

N2 - Existing results on the generalized dissipativity of digital filters are limited to 1-D cases. This brief presents some novel results on the generalized dissipativity of 2-D filters in the discrete Fornasini-Marchesini second (FMS) form. More specifically, we propose a criterion to ascertain that single 2-D filters in the discrete FMS form are 2-D generalized dissipative. Using this result, a condition is established such that the interconnected 2-D filters in the discrete FMS form are 2-D generalized dissipative. Furthermore, the asymptotic stability of unforced interconnected 2-D filters is examined. It is shown that the results developed in our recent work for 1-D filters and in this brief for 2-D filters serve as an overall framework for the generalized dissipativity of digital filters.

AB - Existing results on the generalized dissipativity of digital filters are limited to 1-D cases. This brief presents some novel results on the generalized dissipativity of 2-D filters in the discrete Fornasini-Marchesini second (FMS) form. More specifically, we propose a criterion to ascertain that single 2-D filters in the discrete FMS form are 2-D generalized dissipative. Using this result, a condition is established such that the interconnected 2-D filters in the discrete FMS form are 2-D generalized dissipative. Furthermore, the asymptotic stability of unforced interconnected 2-D filters is examined. It is shown that the results developed in our recent work for 1-D filters and in this brief for 2-D filters serve as an overall framework for the generalized dissipativity of digital filters.

KW - 2-D filter

KW - Fornasini-Marchesini second (FMS) form

KW - generalized dissipativity

KW - interconnected filter

UR - http://www.scopus.com/inward/record.url?scp=84985920629&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84985920629&partnerID=8YFLogxK

U2 - 10.1109/TCSII.2016.2535039

DO - 10.1109/TCSII.2016.2535039

M3 - Article

AN - SCOPUS:84985920629

VL - 63

SP - 893

EP - 897

JO - IEEE Transactions on Circuits and Systems I: Regular Papers

JF - IEEE Transactions on Circuits and Systems I: Regular Papers

SN - 1549-8328

IS - 9

M1 - 7419904

ER -