Global Exponential Stability Analysis of Dynamic Neural Networks with Distributed Delays

Abstract

In this paper, the existence, uniqueness and globally exponential stability of the equilibrium point of a dynamic neural network with distributed delays were studied without assumption of boundedness and differentiability of activation functions. Sufficient criteria for existence, uniqueness and global exponential stability of the equilibrium point of such neural networks were obtained based on the knowledge of M-matrix, topology and Lyapunov stability theory. A test matrix was constructed by the weight matrix and the conditions satisfying activation functions of the neural networks. A neural network has a unique equilibrium point and is globally exponential stable if the test matrix is an M-matrix. Since the criterion is independent of the delays and simplifies the calculation, it is easy to test the conditions of the criterion in practice.

DOI: http://dx.doi.org/10.11591/telkomnika.v11i12.2548