中立型四元数神经网络的稳定性分析  

Stability analysis of quaternion-valued neutral neural networks with time delay

作　　者：树金龙 熊良林[1] 吴涛[1] 郑英丽 SHU Jin-long;XIONG Liang-lin;WU Tao;ZHENG Ying-li(School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650500

出　　处：《云南民族大学学报（自然科学版）》2019年第3期254-262,共9页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(11461082;11601474;61472093);四川省数值模拟重点实验室基金(2017KF002);云南民族大学研究生创新基金(2018YJCXS225)

摘　　要：讨论了中立型四元数神经网络的全局μ稳定问题.用复分解法将中立型四元数神经网络转换为2个复值神经网络,减少了计算复杂度.根据同胚映射理论证明了时滞中立型四元数神经网络系统解的存在唯一性.构造了李雅普诺夫泛函,通过不等式技巧和自由权矩阵方法等分析技巧,分析给出了时滞四元数神经网络系统的全局μ稳定的稳定性判据以及它的一个推论.最后,通过1个数值算例验证文章方法的有效性和结论的正确性.This paper discusses the global-μ stability problem of quaternion-valued neutral neural networks(QVNTNN) with time delay. Firstly, in order to reduce the computational complexity caused by the non-commutability of quaternion matrix multiplication, the QVNTNN system is converted into two complex-valued systems by using the complex decomposition method. Secondly, the existence and uniqueness of the solution of the QVNTNN system with time-delay is proved by the theory of homeomorphism mapping. Then, a new Lyapunov functional is constructed by using the system information, and the inequality is scaled by the inequality technique and the free weight matrix. It has obtained the global-μ stability criterion for the QVNTNN system with time-delay. Finally, a numerical example is given to verify the validity of the method and the correctness of the conclusion.

关 键 词：中立型四元数神经网络 同胚映射理论 李雅普诺夫泛函 全局μ稳定 线性矩阵不等式 

分 类 号：O175[理学—数学]