Robustness analysis of global exponential stability in neural networks evoked by deviating argument and stochastic disturbance

Abstract

This paper studies the robustness of global exponential stability of neural networks evoked by deviating argument and stochastic disturbance. Given the original neural network is globally exponentially stable, we discuss the problem that the neural network is still globally exponentially stable when the deviating argument or both the deviating argument and stochastic disturbance is/are generated. By virtue of solving the derived transcendental equation(s), the upper bound(s) about the intensity of the deviating argument or both of the deviating argument and stochastic disturbance is/are received. The obtained theoretical results are the supplements to the existing literatures on global exponential stability of neural networks. Two numerical examples are offered to demonstrate the effectiveness of theoretical results.

Robustness Analysis of Control Laws in Complex Dynamical Networks Evoked by Deviating Argument

“…Motivated by the above-mentioned discussion, we will find that the presence of deviating arguments will exacerbate difficulties in achieving synchronization of controlled complex dynamical networks (CDNs). In view of the literature [20,21], it is worth considering the influence of the deviation argument on the control method. A new issue arises: can linear control law (nonlinear law) still be kept if a deviation function occurs in the system?…”