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Exponential stability of static neural networks with time delay and impulses

Exponential stability of static neural networks with time delay and impulses

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  • Author(s): S.L. Wu 1, 2 ; K.-L. Li 2 ; T.Z. Huang 3
    • View affiliations
    • Affiliations: 1: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
      2: School of Science, Sichuan University of Science and Engineering, Zigong, People's Republic of China
      3: School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, People's Republic of China
  • Source: Volume 5, Issue 8, 19 May 2011, p. 943 – 951
    DOI:  10.1049/iet-cta.2010.0329 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

In this study, the authors investigate the problem of global exponential stability of static neural networks with time delay and impulses. Three types of impulses are studied: the impulses are input disturbances; the impulses are ‘neutral’ type, that is, they are neither helpful for stability of neural networks nor destabilising; and the impulses are stabilising. For each type of impulses, by using Lyapunov function and Razumikhin-type techniques, sufficient conditions for global exponential stability are established in terms of linear matrix inequalities with respect to suitable classes of impulse time sequences. The new sufficient conditions can explicitly reveal the effects of time delay, impulses etc., on the stability. Numerical results are given to show the less conservatism of the obtained criteria compared with the existing ones.

Inspec keywords: Lyapunov methods; neural nets; asymptotic stability; linear matrix inequalities; delays

Other keywords: Lyapunov function; Razumikhin-type technique; neural network time delay; global exponential stability; linear matrix inequalities; neural network impulse; static neural networks

Subjects: Neural nets; Algebra

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