Stability Analysis And Filtering Research Of Delayed Neural Networks

Neural network is mathematical model that imitates the structure and function of the biological neural network.Recently,neural network plays an important role in the fields of signal processing,image recognition,fixed-point computation,massive high-speed data processing and so on.It is worth noting that neural network is closely related to the dynamical behavior with internal time delay,which usually occurs in the signal transmission of the neural network and its existence is often the source of the system oscillation and instability.Therefore,the study on the stability of delayed neural network has the value of theoretical significance and practical applications.The main work of this paper is to study the stability analysis problem based on time delay neural network.The main contents are as follows:In the first chapter,the research status of delayed neural network system is expounded.The state estimation of delayed neural network and the research status of the data of the dynamic transmission mechanism under limited resources are introduced.Based on some problems of delayed neural network,the relevant knowledge of the main contents is given.In the second chapter,the state estimation of neural network with time varying delay is investigated.Firstly,based on the mathematical model,the state estimation of neural network with time varying delay is established.Then by employing Lyapunov functions and linear matrix inequalities,a sufficient condition for the system asymptotic stability and the existence of the state estimator via the slack variable integral inequality is given.The cone complementarity linearization algorithm is used to obtain the state estimator.Finally,numerical examples are included to illustrate the effectiveness of the proposed method.In the third chapter,we study the hybrid control of neural network with additive time varying delays.The neural network filtering error system is modeled based on the hybrid triggered scheme,and the Zeno phenomenon can be effectively avoided.Sufficient conditions are derived by solving the matrix inequalities for the dissipative filtering problems.Moreover,H_?filters,passive filters,?Q,S,R?-dissipative filters and ₂L-L_?filters are obtained based on the hybrid event triggered mechanism.Finally,two numerical examples are given to illustrate the effectiveness of the proposed method.The fourth chapter summarizes the main work of this paper,and the weakness of this paper is pointed out and the research orientation is given in the future.The major innovations of this paper are listed as follows:?1?the state estimation of delayed neural network is improved by using a relaxation integral inequality;?2?It is the first time that the hybrid control is introduced in the dissipative analysis of neural network with additive time varying delay.