An analysis of CNN settling time

In this paper, the settling time of cellular neural networks (CNN's) is defined and investigated. The settling time is crucial for both simulation and applications of VLSI CNN chips. The computational effort for the numerical integration may be drastically reduced, and CNN programs can be optimized, if a priori knowledge on the settling time is available. For the class of uncoupled CNN's, we present exact analytic solutions, while for propagation-type tasks, tight upper bounds are given. Since the accuracy of template parameter values on a VLSI chip is limited, the effective values may deviate considerably from the nominal values which, in turn, substantially influences the settling time. This influence can be quantified with the help of sensitivity theory. Furthermore, to operate reliably, a template must be jointly optimized for speed and robustness. For uncoupled templates this is readily possible, while for propagating-type tasks, a tradeoff between speed and robustness is the best that can be accomplished. However, considering a sufficient degree of robustness as a constraint rather than as an objective, it is possible to design optimally fast templates analytically.