Robust Stability and Robust Periodicity of Delayed Recurrent Neural Networks With Noise Disturbance

Neural networks suffer from the natural intra- and inter-cellular noise perturbations and environmental fluctuations. Such noises will undoubtedly affect the dynamics of the neural networks both quantitatively and qualitatively. In this paper, we study the effects of noise perturbations on the stability and periodicity of delayed recurrent neural networks. We first derive the mean-square stability conditions for stochastic delayed recurrent neural networks without and with parametric uncertainties, respectively. After that, we study the stochastic periodicity (stability) with disturbance attenuation of delayed recurrent neural networks. The analysis are all based on the Lyapunov-Krasovskii functional approach, and the conditions are all expressed in terms of linear matrix inequalities, which can be easily solved by using the effective convex optimization techniques. Several numerical examples are also given to demonstrate the correctness and effectiveness of the theoretical results