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摘要: 提出一种新的神经网络模型---时滞标准神经网络模型(DSNNM),它由线性动力学系统和有界静态时滞非线性算子连接而成.利用不同的Lyapunov泛函和S方法推导出DSNNM全局渐近稳定性和全局指数稳定性的充分条件,这些条件可表示为线性不等式(LMI)形式.大多数时滞(或非时滞)动态神经网络(DANN)稳定性分析或神经网络控制系统都可以转化为DSNNM,以便用统一的方法进行稳定性分析或镇定控制.从DSNNM应用于时滞联想记忆(BAM)神经网络的稳定性分析以及PH中和过程神经控制器的综合实例,可以看出,得到的稳定性判据扩展并改进了以往文献中的稳定性定理,而且可将稳定性分析推广到非线性控制系统的综合.
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关键词:
- 时滞标准神经网络模型(DSNNM) /
- 线性矩阵不等式(LMI) /
- 稳定性 /
- 广义特征值问题(GEVP) /
- 双向联想记忆(BAM)
Abstract: A novel neural network model, named delayed standard neural network model (DSNNM), is proposed, which is the interconnection of a linear dynamic system and a bounded static delayed nonlinear operator. By combining a number of different Lyapunov functionals with SProcedure, some sufficient conditions for global asymptotic stability and global exponential stability of the DSNNM are derived and formulated as linear matrix inequalities (LMIs). Most delayed (or non-delayed) dynamic artificial neural networks (DANNs) or neuro-control systems can be transformed into DSNNMs so that stability analysis or stabilization synthesis can be done in a unified way. In this paper, DSNNMs are applied to nalyzing the stability of the delayed bidirectional associative memory (BAM) neural net- works and synthesizing the neuro-controllers for the PH neutralization process. The stability criteria obtained turn out to be a generalization of some previous criteria. The analysis ap- proach is further extended to the nonlinear control system.
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