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