Existence and Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Unbounded Distributed Delays
Existence and Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Unbounded Distributed Delays
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DOI：
10.1007/s00034-011-9288-7
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
P. Balasubramaniam;M. Kalpana;R. Rakkiyappan
中科院分区：
文献类型：
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作者：
P. Balasubramaniam;M. Kalpana;R. Rakkiyappan
模糊细胞神经网络（FCNN）结构基于人类认知过程和神经系统建模中的不确定性，为人类专家和经典细胞神经网络（cnn）之间提供了一个接口。研究了具有泄漏项和无界分布延迟的时滞FCNNs平衡点的存在性和全局渐近稳定性分析。基于具有自由权矩阵的Lyapunov-Krasovskii泛函，利用同胚映射原理和线性矩阵不等式（lmi），得到了一组具有泄漏项时滞、时变时滞和无界分布时滞的fcnn的稳定性判据。所提出的结果可以通过MATLAB中的LMI控制工具箱方便地进行检查。此外，众所周知，fcnn的稳定性行为对泄漏项的时间延迟非常敏感。在没有泄漏项的情况下，利用LMI方法采用Lyapunov-Krasovskii泛函导出了一个新的稳定性判据。数值算例说明了所开发技术的有效性和降低的保守性。
Fuzzy cellular neural network (FCNN) structures are based on the uncertainties in human cognitive processes and in modeling neural systems, and they provide an interface between a human expert and classical cellular neural networks (CNNs). In this paper, an existence and global asymptotic stability analysis of the equilibrium point of FCNNs with time delay in the leakage term and unbounded distributed delays is investigated. Based on the Lyapunov-Krasovskii functional with free-weighting matrix, and using the homeomorphism mapping principle and linear matrix inequalities (LMIs), a new set of stability criteria for FCNNs is obtained with time delay in the leakage term, time-varying delays and unbounded distributed delays. The proposed results can be easily checked via the LMI Control Toolbox in MATLAB. Moreover, it is well known that the stability behavior of FCNNs is very sensitive to the time delay in the leakage term. In the absence of the leakage term, a new stability criterion is also derived by employing a Lyapunov-Krasovskii functional using an LMI approach. Numerical examples are provided to illustrate the effectiveness and reduced conservativeness of the developed techniques.