A Discrete-Time Quantized-State Hopfield Neural Network
Annals of Mathematics and Artificial Intelligence
Hopfield Neural Network for Sea Surface Current Tracking from Tiungsat-1 Data
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
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The paper applies several concepts in robust control research such as linear matrix inequalities, edge theorem, parameter-dependent Lyapunov function, and Popov criteria to investigate the stability property of Hopfield-type neural networks. The existence and uniqueness of an equilibrium is formulated as a matrix determinant problem. An induction scheme is used to find the equilibrium. To verify whether the determinant is nonzero for a class of matrix, a numerical range test is proposed. Several robust control techniques in particular linear matrix inequalities are used to characterize the local stability of the neural networks around the equilibrium. The global stability of the Hopfield neural networks is then addressed using a parameter-dependent Lyapunov function technique. All these results are shown to generalize existing results in verifying the existence/uniqueness of the equilibrium and local/global stability of Hopfield-type neural networks