In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all well-defined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.

A learning algorithm based on the decomposition of the A-template into symmetric and anti-symmetric parts is introduced. The performance of the algorithm is investigated in particular for coupled CNNs exhibiting diffusion-like and propagating behavior. 1. INTRODUCTION Cellular neural networks (CNNs) are examples of recurrent networks defined by the following system of differential equations dx ij (t) dt =-x ij (t) + # mn#N ij amn y mn (t) + # mn#N ij bmn u mn + I , where N ij denotes the neighborhood of the ij-th cell for 1 # i # M,1# j # N and y = (|x +1|-|x -1|)/2 . The state, input and output of a cell are defined by x ij , u ij and y ij , respectively. We assume a nearest neighborhood CNN. The output at an equilibrium point, when one exists, is denoted by y # ij .The parameters of a CNN are gathered into the so-called A-template, the B-template and the bias I. In view of learning algorithms, since a CNN is a recurrent neural network, one can apply the lea...

Introduction 1.1 The Classo Bip Cellular Neural Netwo0A In this letter, weco--00b the classo single-layer, spatially invariant cellular neural netwo05 (CNNs) with neighbogho d radiusodi foiu wing thedefinitio given in [1]. The dynamicso the netwo-- isgo verned by a systemo MN di#erentialequatio5b dx i (t) dt = -x i (t)+ # k#N i # a k f(x k (t)) + b k u k # + I (1) where N idenob the neighoig o d o the cell C i , A = {a k } and B = {b k } the feed ack and co tro template parameters, respectively. f() is