An LMI Based State Estimation for Fractional-Order Memristive Neural Networks with Leakage and Time Delays
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An LMI Based State Estimation for Fractional-Order Memristive Neural Networks with Leakage and Time Delays G. Nagamani1 · M. Shafiya1 · G. Soundararajan1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper investigates the state estimation problem for a class of fractional-order memristive neural networks (FOMNNs) with leakage and time delay. The main objective of this study is to construct an efficient estimator such that the state of the corresponding estimation error is globally stable. Distinct to the previous studies, the state estimation problem of FOMNNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global stability of the error system has been derived as a set of solvable linear matrix inequalities. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated. Keywords Caputo’s fractional derivative · Fractional-order memristive neural networks · Lyapunov–Krasvoskii functional · Linear matrix inequalities (LMIs)
1 Introduction Generally, memristor comes from the words: memory and resistor, which was first presumed as the fourth fundamental circuit element by Chua [1]. Specifically speaking, the memristor is a non-volatile memory device which exhibits the dynamics similar to the synaptic connections that alter the synaptic weights in neural networks (NNs) [2]. Due to the memory function involved in the memristor, it works as an ideal material in the process of registering and updating the synaptic weights. Memristive neural networks (MNNs) which was firstly proposed by Yang, Guo, and Wang [3–6] is a novel dynamical NNs which is a combination of the structure of neuronal activation function and memristive connection weights. Based on the features of conventional NNs, the MNNs include a high attractive parallel evaluation
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G. Nagamani [email protected] M. Shafiya [email protected] G. Soundararajan [email protected]
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Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Dindigul, Tamil Nadu, India
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design through which the computation would not extend more while the quantity of data of its mathematical structure increases in the exponential sense [7]. It is widely observed that, the presence of memristors in NNs, makes MNNs to be more complex and produce fruitful dynamical results compared with classical NNs as they have varying history-dependent resistance. Because of its effective computing, MNNs is extensively utilized in many ways, especially in secure communication applications related to encoding and encryption of image transformation [8]. On the parallel perspective, NNs having fractional-order derivatives generally possess boundless memory, which finds an advantage in comparison with common integer-order NNs. In the recent trends, enormous reports have confirmed that fractional calculus has the potential to explore in various areas, especially biological models, medi
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