Abstract
In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model.
Highlights
Over the past two decades, the dynamic analysis for different types of neural networks (NNs), including cellular NNs, recurrent NNs, static NNs, generalized NNs, bi-directional associative memoryNNs, memristor NNs, Cohen-Grossberg NNs, fractional-order NNs, have received remarkable attention due to their successful applications [1,2,3,4,5,6,7,8]
The stochastic effects must be taken into consideration in stability analysis of NNs
In this sub-section, we present the sufficient conditions for the existence, uniqueness, as well as global asymptotic stability of the considered complex-valued neural network (CVNN) model
Summary
Over the past two decades, the dynamic analysis for different types of neural networks (NNs), including cellular NNs, recurrent NNs, static NNs, generalized NNs, bi-directional associative memory. NNs, memristor NNs, Cohen-Grossberg NNs, fractional-order NNs, have received remarkable attention due to their successful applications [1,2,3,4,5,6,7,8] In this domain, the Hopfield Neural Network (HNN) has been considered as an attractive model due to its robust mathematical capability [9]. It should be noted that the robust stability issue with respect to uncertain stochastic complex-valued Hopfield neural networks (USCVHNNs) with time delays is yet to be fully investigated. This forms the motivation of the present research.
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