Title :
Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable
Author :
Takahashi, Norikazu ; Nishi, Tetsuo
Author_Institution :
Dept. of Comput. Sci. & Commun. Eng., Kyushu Univ., Fukuoka
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
Keywords :
cellular neural nets; linear systems; stability; CNN; cellular neural networks; complete stability; global dynamical behavior; piecewise-linear dynamical system; piecewise-linear function; planar dynamical systems; self-coupling coefficients; Cellular neural networks; Circuit stability; Computer science; Differential equations; Image processing; Neural networks; Piecewise linear techniques; Recurrent neural networks; Stability analysis; Sufficient conditions; Cellular neural networks (CNNs); complete stability; planar dynamical systems;
Journal_Title :
Circuits and Systems II: Express Briefs, IEEE Transactions on
DOI :
10.1109/TCSII.2006.876466
