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Existence and Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Unbounded Distributed Delays

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Abstract

Fuzzy cellular neural network (FCNN) structures are based on the uncertainties in human cognitive processes and in modeling neural systems, and they provide an interface between a human expert and classical cellular neural networks (CNNs). In this paper, an existence and global asymptotic stability analysis of the equilibrium point of FCNNs with time delay in the leakage term and unbounded distributed delays is investigated. Based on the Lyapunov-Krasovskii functional with free-weighting matrix, and using the homeomorphism mapping principle and linear matrix inequalities (LMIs), a new set of stability criteria for FCNNs is obtained with time delay in the leakage term, time-varying delays and unbounded distributed delays. The proposed results can be easily checked via the LMI Control Toolbox in MATLAB. Moreover, it is well known that the stability behavior of FCNNs is very sensitive to the time delay in the leakage term. In the absence of the leakage term, a new stability criterion is also derived by employing a Lyapunov-Krasovskii functional using an LMI approach. Numerical examples are provided to illustrate the effectiveness and reduced conservativeness of the developed techniques.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute, Deemed University, Gandhigram, 624 302, Tamilnadu, India

    P. Balasubramaniam, M. Kalpana & R. Rakkiyappan

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  1. P. Balasubramaniam
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  2. M. Kalpana
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  3. R. Rakkiyappan
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Correspondence to P. Balasubramaniam.

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Balasubramaniam, P., Kalpana, M. & Rakkiyappan, R. Existence and Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Unbounded Distributed Delays. Circuits Syst Signal Process 30, 1595–1616 (2011). https://doi.org/10.1007/s00034-011-9288-7

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  • DOI: https://doi.org/10.1007/s00034-011-9288-7

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