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Neutral-Type and Mixed Delays in Fractional-Order Neural Networks: Asymptotic Stability Analysis
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DOI：10.3390/fractalfract7010036.png)
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Abstract
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The lack of a conventional Lyapunov theory for fractional-order (FO) systems makes it difficult to study the dynamics of fractional-order neural networks (FONNs). Instead, the existing literature derives necessary conditions for various dynamic properties of FONNs using Halanay-type lemmas. However, when these lemmas are used, the results are frequently more conservative than those produced for integer-order neural networks (NNs). In order to provide sufficient criteria that are less conservative than those found in other research, a novel application of the Halanay-type lemma is made within this study. Thus, for extremely general FONNs containing neutral-type, time-varying, and distributed delays, sufficient conditions presented by way of linear matrix inequalities (LMIs) and algebraic inequalities are achieved. For the FO scenario, a model this broad and including so many different kinds of delays is developed for the first time. Additionally, a novel form of Lyapunov-like function is built, which results in less stringent algebraic inequalities. One of the first times in the setting of FONNs, the free-weighting matrix method is also used to further lower the conservativeness of the obtained conditions. Based on different Lyapunov-type functions, three theorems are developed regarding the asymptotic stability of the proposed networks. Three numerical simulations are used to demonstrate the theoretical developments.
Keywords:
fractional-order neural networks (FONNs)
neutral-type delays
distributed delays
mixed delays
asymptotic stability
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