Discrete-time delayed standard neural. network model and its application

作者：Liu MQ^*

来源：Science in China - Series F: Information Sciences , 2006, 49(2): 137-154.

DOI：10.1007/s11432-006-0137-4

• delayed standard neural network model (DSNNM)
• linear matrix inequality (LMI)
• stability
• generalized eigenvalue problem (GEVP)
• discrete-time
• nonlinear control

A novel neural network model, termed the discrete-time delayed standard neural network model (DDSNNM), and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks (RNNs) and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed (or non-delayed) nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks (CNNs) and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.

• 出版日期2006-4
• 单位浙江大学