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Stability Conditions of Delayed Recurrent Neural Networks with Positive Linear Activation Functions

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Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

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Abstract

By using the positive linearity of the activation functions of neurons in recurrent neural networks, and by adopting the method of decomposing the state space to sub-regions, the mathematical equations of delayed recurrent 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.

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Author information

Authors and Affiliations

  1. School of Electrical and Information Engineering, Zhongyuan University of Technology, Zhengzhou, Henan, 450007, China

    Dongyun Wang & Yan Wang

Authors
  1. Dongyun Wang
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  2. Yan Wang
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Editor information

Editors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

    Nian Zhang

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Wang, D., Wang, Y. (2009). Stability Conditions of Delayed Recurrent Neural Networks with Positive Linear Activation Functions. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_34

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  • DOI: https://doi.org/10.1007/978-3-642-01507-6_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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