Parameter learning or design is a key issue in cellular neural network (CNN
) theory. If the CNN is implemented as an analog VLSI chip, additional cons
traints are posed due to its restricted accuracy. Only robust parameters wi
ll still guarantee the correct network behavior. We present an analytical d
esign approach for the class of bipolar CNNs 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 inequali
ties can be analytically solved for the most robust template by simple matr
ix algebra. Focusing on a particular implementation of the CNN universal ch
ip, we demonstrate that the proposed method can cope with the manufacturing
inaccuracies.