Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis

Houduo Qi, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

56 Citations (Scopus)


In this paper, we obtain new sufficient conditions ensuring existence, uniqueness, and global asymptotic stability (GAS) of the equilibrium point for a general class of delayed neural networks (DNNs) via nonsmooth analysis, which makes full use of the Lipschitz property of functions defining DNNs. Based on this new tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then those results are applied to show that existence assumptions on the equilibrium point in some existing sufficient conditions ensuring GAS are actually unnecessary; and some strong assumptions such as the boundedness of activation functions in some other existing sufficient conditions can be actually dropped. Finally, we derive some new sufficient conditions which are easy to check. Comparison with some related existing results is conducted and advantages are illustrated with examples. Throughout our paper, spectral properties of the matrix (A + Aτ) play an important role, which is a distinguished feature from previous studies. Here, A and Aτare, respectively, the feedback and the delayed feedback matrix defining the neural network under consideration.
Original languageEnglish
Pages (from-to)99-109
Number of pages11
JournalIEEE Transactions on Neural Networks
Issue number1
Publication statusPublished - 1 Jan 2004


  • Equilibrium point
  • Generalized Jacobian
  • Global asymptotic stability (GAS)
  • Homeomorphism
  • Invertibility
  • Lyapunov functions
  • Neural networks (NNs)
  • Nonsingularity
  • Spectral norm
  • Spectral radius

ASJC Scopus subject areas

  • Software
  • General Medicine
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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