Chinese Journal of Intelligent Science and Technology ›› 2020, Vol. 2 ›› Issue (1): 80-87.doi: 10.11959/j.issn.2096-6652.202009

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Stability analysis of commutative quaternion valued neural network with time varying delays

Dongyuan LIN1,Xiaofeng CHEN1,Wentao SUN2(),Weikai LI3,Yannan XIA1   

  1. 1 College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China
    2 School of Science,Tibet University,Lhasa 850000,China
    3 College of Computer Science &Technology,Nanjing University of Aeronautics &Astronautics,Nanjing 210016,China
  • Revised:2020-02-19 Online:2020-03-20 Published:2020-04-10
  • Supported by:
    Natural Science Foundation of Chongqing(cstc2017jcyjAX0082);Natural Science Foundation of Chongqing(cstc2018jcyjAX0606);Scientific and Technology Research Program of Chongqing Municipal Education Commission(KJQN201900701)

Abstract:

Because the traditional quaternion multiplication does not meet the commutative law,a kind of commutative quaternion was introduced,and a commutative quaternion valued neural network (CQVNN) was established,and the asymptotic stability of the CQVNN was studied.In the course of research,the CQVNN were decomposed into four real-valued neural networks.Then,through the topological degree theory,the traditional Lyapunov stability theory and the inequality theory,the conditions for the existence and uniqueness of the equilibrium point of CQVNN and the linear matrix inequality (LMI) conditions for the asymptotically stable of equilibrium point were obtained.Finally,a numerical example was given to verify the validity of the conclusion.

Key words: commutative quaternion, delayed neural network, asymptotically stability

CLC Number: 

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