A new approach to stability of neural networks with time-varying delays
The stability of neural networks is a prerequisite for successful applications of the networks as either associative memories or optimization solvers. Because the integration and communication delays are ubiquitous, the stability of neural networks with delays has received extensive attention. However, the approach used in the previous investigation is mainly based on Liapunov's direct method. Since the construction of Liapunov function is very skilful, there is little compatibility among the existing results. In this paper, we develop a new approach to stability analysis of Hopfield-type neural networks with time-varying delays by defining two novel quantities of nonlinear function similar to the matrix norm and the matrix measure, respectively. With the new approach, we present sufficient conditions of the stability, which are either the generalization of those existing or new. The developed approach may be also applied for any general system with time delays rather than Hopfield-type neural networks.
time-varying delay hopfield-type neural networks exponential stability minimal lipschitz constant nonlinear lipschitz measure