With Time-varying Delay Discrete-time Neural Network Stability Analysis

The stability of neural networks has been widespread concern for their extensive applications, such as image processing, fixed point computation, pattern recognition, information processing and control theory and other aspects of the application. The stability characteristics of the signal in the optimization, pattern recognition, signal processing and other fields, promotes the designation of the neural network model with only one point of global asymptotic stability. In this dissertation, Lyapunov second method is adopted to analyze the asymptotic stability of discrete time neural networks with a variable delay.In this dissertation, the asymptotic stability of discrete time neural networks with a variable delay is studied, and the following main results are obtained.(1) Much more flexible asymptotic stability criteria has been achieved for the linear discrete neural networks with interval time delays. Numerical simulations show the effectiveness and practicality of the criteria.(2) For the linear discrete neural networks with time varying delay, conservative and more open global asymptotic stability criteria is achieved, based on the construction of Lyapunov function and delays'segmenting, which decreases the number of variable. Numerical simulations show the feasibility and performance advantages.(3) The determination of a negative matrix is introduced to the research on linear discrete neural networks with time varying delay, which reduces the conservation of the criteria and induces more open global asymptotic stability criteria. Numerical simulations show the feasibility of this method.