Stability analysis of dynamical neural networks

Abstract

In this paper, we use the matrix measure technique to study the stability of dynamical neural networks. Testable conditions for global exponential stability of nonlinear dynamical systems and dynamical neural networks are given. It shows how a few well-known results can be unified and generalized in a straightforward way. Local exponential stability of a class of dynamical neural networks is also studied; we point out that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks are obtained.