Asymptotic stability for neural networks with mixed time-delays: The discrete-time case

作者：Liu Yurong^*; Wang Zidong; Li Xiaohui

来源：Neural Networks, 2009, 22(1): 67-74.

DOI：10.1016/j.neunet.2008.10.001

• Discrete-time neural networks
• Stochastic neural networks
• Asymptotic stability
• Discrete time-delays
• Distributed time-delays
• Lyapunov-Krasovskii functional
• Linear matrix inequality

This paper is concerned with the stability analysis problem for a new class of discrete-time recurrent neural networks with mixed time-delays. The mixed time-delays that consist of both the discrete and distributed time-delays are addressed, for the first time, when analyzing the asymptotic stability for discrete-time neural networks. The activation functions are not required to be differentiable or strictly monotonic. The existence of the equilibrium point is first proved under mild conditions. By Constructing a new Lyapnuov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the discrete-time neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same class of neural networks but with state-dependent Stochastic disturbances. All the conditions obtained are expressed in terms of LMIs whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. A Simulation example is presented to show the usefulness of the derived LMI-based stability condition.

• 出版日期2009-1
• 单位扬州大学