Nonlinear measures: A new approach to exponential stability analysis for Hopfield-type neural networks

In this paper, a new concept called nonlinear measure is introduced to quan tify stability of nonlinear systems in the way similar to the matrix measur e for stability of linear systems. Based on the new concept, a novel approa ch for stability analysis of neural networks is developed. With this approa ch, a series of new sufficient conditions for global and focal exponential stability of Hopfield type neural networks is presented, which generalizes those existing results. By means of the introduced nonlinear measure, the e xponential convergence rate of the neural networks to stable equilibrium po int is estimated, and, for local stability, the attraction region of the st able equilibrium point is characterized. The developed approach tan be gene ralized to stability analysis of other general nonlinear systems.