| 引用本文: | 徐晓惠,张继业,施继忠,任松涛.脉冲干扰时滞复值神经网络的稳定性分析[J].哈尔滨工业大学学报,2016,48(3):166.DOI:10.11918/j.issn.0367-6234.2016.03.028 |
| XU Xiaohui,ZHANG Jiye,SHI Jizhong,REN Songtao.Stability analysis of delayed complex-valued neural networks with impulsive disturbances[J].Journal of Harbin Institute of Technology,2016,48(3):166.DOI:10.11918/j.issn.0367-6234.2016.03.028 |
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| 摘要: |
| 为分析脉冲干扰因素对复值神经网络动态行为的影响，研究一类具有混合时滞和脉冲干扰的复值神经网络的平衡点的全局指数稳定性.在假定神经元状态、激活函数以及关联矩阵定义在复数域的情况下，利用M矩阵理论、向量Lyapunov函数法以及数学归纳法，分析确保该系统平衡点的存在性、唯一性以及全局指数稳定性的充分条件，并给出了指数收敛率，最后通过一个数值仿真算例验证了所得结论的正确性.结果表明：时滞和脉冲干扰均会降低神经元状态的指数收敛速度，所建立的稳定性判据推广了现有结论.
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| 关键词: 复值神经网络 脉冲干扰 混合时滞 全局指数稳定性 矢量Lyapunov函数 |
| DOI：10.11918/j.issn.0367-6234.2016.03.028 |
| 分类号:TP391 |
| 文献标识码:A |
| 基金项目:国家自然科学基金(4,2, 4,1)；四川省青年科技创新研究团队专项计划 (2015TD0021)；教育部“春晖计划”合作科研项目(Z2014075)；浙江省自然科学基金(LY14E08006). |
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| Stability analysis of delayed complex-valued neural networks with impulsive disturbances |
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XU Xiaohui1, ZHANG Jiye2, SHI Jizhong3, REN Songtao1
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(1.School of Automobile and Transportation, Xihua University, 610039 Chengdu, China; 2.National Traction Power Laboratory（Southwest Jiaotong University）, 610031 Chengdu, China; 3. College of Engineering, Zhejiang Normal University, 321004 Jinhua, Zhejiang,China)
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| Abstract: |
| To investigate the effect of impulsive disturbances on the dynamical behavior of the equilibrium point of complex-valued neural networks, the globally exponential stability of a class of the system with mixed delays and impulsive disturbances was studied in this paper. Assume that the neuron states, activation functions and interconnected matrix were defined in the complex domain. Some sufficient conditions for assuring the existence, uniqueness and globally exponential stability of the equilibrium point of the system were obtained by applying the M matrix theory, the mathematical induction and the vector Lyapunov function methods. Meanwhile, the exponential convergence rate was proposed. It can be concluded from the established sufficient conditions that the exponential convergence rate of the neurons is reduced by both time delays and the impulsive disturbances. The stability criteria established in this paper generalize the existing results. Finally, a numerical example with simulations was given to show the correctness of the obtained results.
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| Key words: complex-valued neural networks impulsive disturbances mixed delays globally exponential stability vector Lyapunov function |
