$L\infty$ Analysis and State-Feedback Control of Hopfield Networks

A nonsymmetric 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 brief, we adopt the Lur'e-Postnikov systems approach to analyze the induced L
_∞
gain of generalized Hopfield networks. A state-feedback control is then designed to accomplish the L
_∞
-type performance for Hopfield networks. The results are illustrated through numerical examples.