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Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. (English) Zbl 1217.34116
Summary: A class of bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays is formulated to study the global asymptotic stability. This approach is based on the Lyapunov-Krasovskii functional with free-weighting matrices. Using linear matrix inequality (LMI), a new set of stability criteria for BAM FCNNs with time delay in the leakage term, discrete and unbounded distributed delays is obtained. Also, the stability behavior of BAM FCNNs is very sensitive to the time delay in the leakage term. In the absence of a leakage term, a new stability criteria is also derived by employing a Lyapunov-Krasovskii functional and using the LMI approach. Our results establish a new set of stability criteria for BAM FCNNs with discrete and unbounded distributed delays. Numerical examples are provided to illustrate the effectiveness of the developed techniques.
##### MSC:
 34K20 Stability theory of functional-differential equations 34K36 Fuzzy functional-differential equations 92B20 General theory of neural networks (mathematical biology)
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