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Discrete-time delayed standard neural network model and its application

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Abstract

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.

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Authors and Affiliations

  1. School of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China

    Liu Meiqin

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  1. Liu Meiqin
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Liu, M. Discrete-time delayed standard neural network model and its application. SCI CHINA SER F 49, 137–154 (2006). https://doi.org/10.1007/s11432-006-0137-4

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  • DOI: https://doi.org/10.1007/s11432-006-0137-4

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