Stability and Robust Stability of Stochastic Reaction–Diffusion Neural Networks With Infinite Discrete and Distributed Delays
Yin Sheng, Hao Zhang, Zhigang Zeng · IEEE Transactions on Systems Man and Cybernetics Systems · 2018
This paper investigates the φ-type stability and robust stability for a general class of stochastic reaction-diffusion neural networks (SRDNNs) with Dirichlet boundary conditions, infinite discrete time-varying delays, and infinite continuously distributed delays. By virtue of inequality techniques, properties of M-matrix, and theories of stochastic analysis, several sufficient criteria are obtained to guarantee the almost sure φ-type stability, pth moment φ-type stability, and φ-type robust stability of the underlying SRDNNs with hybrid unbounded time delays. With appropriate choices of the function φ, the φ-type stability reduces to the exponential stability, polynomial stability, and logarithmic stability. Additionally, the developed results herein include some existing ones as special cases. A numerical simulation is performed to substantiate the effectiveness and superiority of the theoretical analysis.