Absolute Stability Analysis for a Class of Discrete-Time Neural Networks

Abstract − The asymptotic behavior of a class discrete-time Hopfield neural network is studied in this paper. Some properties for this class discrete-time neural network, such as the boundedness of motion trajectory, the uniqueness and the absolute stability of equilibrium point etc, are obtained. In this paper, the sufficient conditions related to the existence of unique equilibrium point and absolute stability of equilibrium point for the discrete-time Hopfield neural networks are discussed. These criteria to test absolute stability of the equilibrium point of this neural network model require verification of the definiteness of a certain matrix or verification of a certain inequality. These results can be used for the synthesis procedures for discrete-time Hopfield neural networks.