Delay-Dependent and Delay-Independent Stability Conditions of Delayed Cellular Neural Networks

  • Wudai Liao
  • Dongyun Wang
  • Yulin Xu
  • Xiaoxin Liao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4232)


By using the saturation linearity of the output functions of neurons in cellular neural networks, and by adopting the method of decomposing the state space to sub-regions, the mathematical equations of delayed cellular neural networks are rewritten to be the form of linear differential difference equations in the neighbourhood of each equilibrium, which is an interior point of some sub-region. Based on this linear form and by using the stability theory of linear differential difference equations and the tool of M-matrix, delay-dependent and delay-independent stability algebraic criteria are obtained. All results obtained in this paper need only to compute the eigenvalues of some matrices or to examine the matrices to be M-matrix or to verify some inequalities to be holden.


Interior Point Asymptotic Stability Output Function Negative Real Part Cellular Neural Network 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wudai Liao
    • 1
  • Dongyun Wang
    • 1
  • Yulin Xu
    • 1
  • Xiaoxin Liao
    • 2
  1. 1.Zhongyuan University of TechnologyZhengzhou HenanChina
  2. 2.Huazhong University of Science and TechnologyWuhan HubeiChina

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