Global Exponential Stability of Neural Networks with Time-varying Delays
Fen Wang · Control Engineering of China · 2009
By M-matrix theory,homeomorphism theory and inequality technique,we study the existence and uniqueness of the equilibrium point of a kind of neural network with time-varying delays.Applying M-matrix theory and reduction to absurdity,we obtain the sufficient conditions of the global exponential stability of the uniqueness equilibrium point,by M-matrix theory,reduction to absurdity and inequality technique.Based on the criteria,the global exponential stability of the neural networks can be obtained by judging whether the matrix constructed by the weighed coefficients,self-feedback functions and activation functions of the system is an M-matrix.The criteria can be checked by Matlab.A numerical example is provided to illustrate the effectiveness of the obtained criteria.