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.

Abstract—An important property of cellular neural networks (CNN’s) is the binary output property, that, when the self-feedback is greater than one, the final activations are 61. This brief considers the generalization of this property to networks with sigmoidal output functions. It is shown that in this case the property cannot be stated without reference to the cross feedback, and conditions are found under which the property remains valid. I.