L-infinity analysis of Hopfield networks

Abstract

A non symmetric version of Hopfield networks subject to bounded disturbances is considered. Such networks arise in the context of visuo-motor control loops and may, therefore, be used to mimic their complex behavior. In this paper, we adopt the Lur'e-Postnikov systems approach to analyze the induced L∞8 gain of generalized Hopfield networks. The results are illustrated via a simple numerical example.