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首页> 外文期刊>Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on >A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays
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A Unified Approach to the Stability of Generalized Static Neural Networks With Linear Fractional Uncertainties and Delays

机译：具有线性分数不确定性和时滞的广义静态神经网络稳定性的统一方法

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摘要

In this paper, the robust global asymptotic stability (RGAS) of generalized static neural networks (SNNs) with linear fractional uncertainties and a constant or time-varying delay is concerned within a novel input–output framework. The activation functions in the model are assumed to satisfy a more general condition than the usually used Lipschitz-type ones. First, by four steps of technical transformations, the original generalized SNN model is equivalently converted into the interconnection of two subsystems, where the forward one is a linear time-invariant system with a constant delay while the feedback one bears the norm-bounded property. Then, based on the scaled small gain theorem, delay-dependent sufficient conditions for the RGAS of generalized SNNs are derived via combining a complete Lyapunov functional and the celebrated discretization scheme. All the results are given in terms of linear matrix inequalities so that the RGAS problem of generalized SNNs is projected into the feasibility of convex optimization problems that can be readily solved by effective numerical algorithms. The effectiveness and superiority of our results over the existing ones are demonstrated by two numerical examples.
机译：在本文中，具有线性分数不确定性和恒定或时变时滞的广义静态神经网络（SNN）的鲁棒全局渐近稳定性（RGAS）在新型输入输出框架内受到关注。假定模型中的激活函数比通常使用的Lipschitz型函数满足更一般的条件。首先，通过四个步骤的技术改造，将原始的广义SNN模型等效地转换为两个子系统的互连，其中前向子系统是具有恒定延迟的线性时不变系统，而反馈子系统则具有范数界。然后，基于缩放的小增益定理，通过结合完整的Lyapunov函数和著名的离散化方案，为广义SNN的RGAS导出依赖于延迟的充分条件。所有结果均以线性矩阵不等式给出，因此广义SNN的RGAS问题被投影到凸优化问题的可行性上，而凸优化问题可以通过有效的数值算法轻松解决。通过两个数值例子证明了我们的结果优于现有结果的有效性和优越性。

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