Stability Analysis Of A Class Of Neural Networks With Delay

Based on the tremendous impact of stability theory on cell neural networks, this thesis tries to illustrate the application of the projection system dynamics. It discusses a novel proof method which focuses on the exponential stability of a class of time-delayed projection neural networks and on the neutral global asymptotic stability of the discrete and distributed delay cellular neural networks.First, considering a class of delayed projection neural network model, this thesis segments the state variable into sub-blocks in accordance with the characteristics of these neural networks. Then, it acquires the sufficient conditions to get the stability of neural network system by constructing Lyapunov functional. Under appropriate initial conditions, it shows the advantages of the conditions we obtain if the given conditions of stability has nothing to do with some of the faster bloc matrix. Through the further study of the multi-delay stability of cellular neural networks, this thesis gets a number of general principles which determine the equilibrium and global exponential stability of the network.Second, this thesis studies the neutral global asymptotic stability of the distributional delayed and discrete cellular neural networks. Firstly, this thesis proves the existence and uniqueness of the system equilibrium point by using the topological degree theory and related knowledge. Then, this thesis establishes the criterion of the global exponential stability of trivial solution to the discrete and distributed time-delay system of neutral type neural networks by constructing a Lyapunov-Krasovskii functional. In this thesis, only one M-matrix is required to control, which reduces the conditions needed by some previous studies that require spectrum; meanwhile, some results of the previous studies are also modified in this thesis. The proving methods in this thesis is more innovative while compared with the previous ones.