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A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks

IEEE transaction on neural networks and learning systems, 2014-07, Vol.25 (7), p.1229-1262

ISSN: 2162-237X ;EISSN: 2162-2388 ;DOI: 10.1109/TNNLS.2014.2317880 ;CODEN: ITNNAL

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  • Title:
    A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks
  • Author: Zhang, Huaguang ; Wang, Zhanshan ; Liu, Derong
  • Subjects: Biological neural networks ; Cohen--Grossberg neural networks ; Delays ; discrete delay ; distributed delays ; Hopfield neural networks ; linear matrix inequality (LMI) ; Lyapunov diagonal stability (LDS) ; M-matrix ; Neurons ; Recurrent neural networks ; robust stability ; stability ; Stability criteria
  • Is Part Of: IEEE transaction on neural networks and learning systems, 2014-07, Vol.25 (7), p.1229-1262
  • Description: Stability problems of continuous-time recurrent neural networks have been extensively studied, and many papers have been published in the literature. The purpose of this paper is to provide a comprehensive review of the research on stability of continuous-time recurrent neural networks, including Hopfield neural networks, Cohen-Grossberg neural networks, and related models. Since time delay is inevitable in practice, stability results of recurrent neural networks with different classes of time delays are reviewed in detail. For the case of delay-dependent stability, the results on how to deal with the constant/variable delay in recurrent neural networks are summarized. The relationship among stability results in different forms, such as algebraic inequality forms, M-matrix forms, linear matrix inequality forms, and Lyapunov diagonal stability forms, is discussed and compared. Some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed. Concluding remarks and future directions of stability analysis of recurrent neural networks are given.
  • Publisher: IEEE
  • Language: English
  • Identifier: ISSN: 2162-237X
    EISSN: 2162-2388
    DOI: 10.1109/TNNLS.2014.2317880
    CODEN: ITNNAL
  • Source: IEEE Open Access Journals
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