A stability criterion for Hopfield networks based on Popov theorem

A Hopfield network is considered as a nonlinear system with multiples nonlinearities (so called Lurie systems). A frequency domain criterion is formulated to prove global asymptotic stability of the equilibrium point of the system, this condition is expressed as a inequality over the whole range of frequency. This known result is applied to analyse the global asymptotic stability of a Hopfield network, obtaining conditions for testing the stability of the equilibrium points and their regions of attractions. These conditions do not require symmetric interconnection matrices.<
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