Stability And Stabilization Of Discrete-time BAM Neural Networks With Multiple Time-varying Delays

Global exponential stability criteria and a design method of state observer for discrete-time BAM(Bidirectional Associative Memory)neural networks with multiple time-varying delays are presented in this thesis.Moreover,the state feedback stabilization problem of discrete-time Cohen-Grossberg type BAM neural networks with multiple time-varying delays is studied,and a controller design method which is easily put into practice is proposed.The details are as follows:Firstly,the development of(time-delay)neural networks is briefly described,and the research status of delayed BAM neural networks and delayed Cohen-Grossberg type BAM neural networks are briefed.Secondly,For the discrete-time BAM neural networks with multiple discrete time-varying delay and mixed time-delays,a mathematical induction method is proposed to establish the global exponential stability criteria of LMI(Linear Matrix Inequality)form,and the stability criteria which only depend on the system parameters are deduced.The valid of the proposed method is checked by using standard software tool.This method is directly based on the definition of global exponential stability,and does not involve the construction of any Lyapunov-Krasovskii functional.Thirdly,according to the definition of global exponential stability and the properties of Moore-Penrose inverse of the matrix,the state estimation problem of discrete-time BAM neural networks with multiple time-varying delays is studied.The global expo-nential stability conditions of error system are given.Thereby,a design method of the state observer neural for the networks under consideration is proposed.Furthermore,the design method of observer is extended to discrete-time BAM neural networks with mixed delays.Finally,the state feedback stabilization problem for a class of discrete-time Cohen-Grossberg type neural networks with multiple time-varying delays is studied.By using the mathematical induction method,the dependent and delay-independent conditions are given to ensure the global exponential stability of the resulting closed-loop system.These conditions only involve solving a few simple LMIs or calculating the spectrum of a constant matrix,which can be easily verified by using standard software tool such as MATLAB.On this basis,the state feedback controllers of the considered a class of discrete-time Cohen-Grossberg type BAM are proven.A numerical example is given to verify that the designed state feedback controller is effective.