On Exponential Stability of Delayed Discrete-Time Complex-Valued Inertial Neural Networks

This article tackles the global exponential stability for a class of delayed complex-valued inertial neural networks in a discrete-time form. It is assumed that the activation function can be separated explicitly into the real part and imaginary part. Two methods are employed to deal with the stability issue. One is based on the reduced-order method. Two exponential stability criteria are obtained for the equivalent reduced-order network with the generalized matrix-measure concept. The other is directly based on the original second-order system. The main theoretical results complement each other. Some comparisons with the existing works show that the results in this article are less conservative. Two numerical examples are given to illustrate the validity of the main results.