Robustness Analysis For Global Exponential Stability Of Recurrent Neural Networks

In this paper, we analyze the robustness of global exponential stability of stochastic recurrent neural networks subjected to random disturbances, time delays and parameter uncertainties in connection weight matrices. The novel exponential stability criteria for the perturbed stochastic recurrent neural networks are derived. The upper bounds of the noise intensity, time delays and parameter uncertainties in connection weight matrices are characterized by solving transcendental equations containing adjustable parameters. Through the selection of the adjustable parameters, the upper bounds are improved. On the other hand, we deduce that there are the intensity of noise which make the globally exponentially stable recurrent neural networks even more stable. It shows that our results generalize and improve the corresponding results of recent works. In addition, some numerical examples are given to show the effectiveness of the results we obtained.Chapter 2 considers the recurrent neural networks and delayed recurrent neural networks model subjected to noise. By using coefficients of global exponential stability, we could deduce that further results on robustness analysis of global exponential stability of recurrent neural networks with random disturbances. Meanwhile, we could deduce that noise is able to further express exponential decay for the perturbed recurrent neural networks without losing global stability.Chapter 3 investigates the time delays impact on stability for stochastic recurrent neural networks. We first discuss drift term of system with time delays, we could deduce that further results on robustness analysis of global exponential stability of recurrent neural networks directly by estimating the upper bounds of time delays. In addition, we consider that time delays are added into both drift and diffusion terms of system, we can also deduce that the perturbed stochastic recurrent neural networks are globally exponentially stable.Chapter 4 studies the parameter uncertainties in connection weight matrices impact on stability for stochastic recurrent neural networks. The further results on robustness analysis of global exponential stability of recurrent neural networks with parameter uncertainties in connection weight matrices are derived. On the other hand,we deduce that the perturbed stochastic delayed recurrent neural networks are globally exponentially stable.Finally, Chapter 5 summarizes the research conclusions and points out the problems to be further researched in the future.