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Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

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Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand
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Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
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Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, Thailand
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Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Tamil Nadu-600 062, India
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Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 422; https://doi.org/10.3390/math8030422
Received: 13 February 2020 / Revised: 9 March 2020 / Accepted: 11 March 2020 / Published: 14 March 2020
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results. View Full-Text
Keywords: stability; stabilization; memristor; fractional calculus; quaternion-valued neural networks stability; stabilization; memristor; fractional calculus; quaternion-valued neural networks
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MDPI and ACS Style

Rajchakit, G.; Chanthorn, P.; Kaewmesri, P.; Sriraman, R.; Lim, C.P. Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks. Mathematics 2020, 8, 422.

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