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Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable

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2 Author(s)
Takahashi, N. ; Dept. of Comput. Sci. & Commun. Eng., Kyushu Univ., Fukuoka ; Nishi, T.

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

Published in:

Circuits and Systems II: Express Briefs, IEEE Transactions on  (Volume:53 ,  Issue: 8 )

Date of Publication:

Aug. 2006

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