Necessary and sufficient condition for a class of planar dynamical systems related to CNNs to be completely stable

Norikazu Takahashi, Tetsuo Nishi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.

Original languageEnglish
Pages (from-to)727-733
Number of pages7
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Volume53
Issue number8
DOIs
Publication statusPublished - Aug 2006
Externally publishedYes

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Cellular neural networks
Dynamical systems

Keywords

  • Cellular neural networks (CNNs)
  • Complete stability
  • Planar dynamical systems

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

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AB - We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.

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