Stability of CNN with trapezoidal activation function

Abstract

This paper presents the stability conditions of cellular neural network (CNN) scheme employing a new nonlinear activation function, called trapezoidal activation function (TAF). The new CNN structure can classify linearly nonseparable data points and realize Boolean operations (including XOR) by using only a single-layer CNN. In order to simplify the stability analysis, a feedback matrix W is defined as a function of the feedback template A and 2D equations are converted to 1D equations. The stability conditions of CNN with TAF are investigated and a sufficient condition for the existence of a unique equilibrium and global asymptotic stability is derived.