Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks
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...
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/422 |
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doaj-0d2cc7a76209463ca9fc22a72529aaa22020-11-25T01:30:04ZengMDPI AGMathematics2227-73902020-03-018342210.3390/math8030422math8030422Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural NetworksGrienggrai Rajchakit0Pharunyou Chanthorn1Pramet Kaewmesri2Ramalingam Sriraman3Chee Peng Lim4Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, ThailandResearch Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, ThailandVel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Tamil Nadu-600 062, IndiaInstitute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, AustraliaThis 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.https://www.mdpi.com/2227-7390/8/3/422stabilitystabilizationmemristorfractional calculusquaternion-valued neural networks |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Grienggrai Rajchakit Pharunyou Chanthorn Pramet Kaewmesri Ramalingam Sriraman Chee Peng Lim |
| spellingShingle |
Grienggrai Rajchakit Pharunyou Chanthorn Pramet Kaewmesri Ramalingam Sriraman Chee Peng Lim Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks Mathematics stability stabilization memristor fractional calculus quaternion-valued neural networks |
| author_facet |
Grienggrai Rajchakit Pharunyou Chanthorn Pramet Kaewmesri Ramalingam Sriraman Chee Peng Lim |
| author_sort |
Grienggrai Rajchakit |
| title |
Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks |
| title_short |
Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks |
| title_full |
Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks |
| title_fullStr |
Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks |
| title_full_unstemmed |
Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks |
| title_sort |
global mittag–leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2020-03-01 |
| description |
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. |
| topic |
stability stabilization memristor fractional calculus quaternion-valued neural networks |
| url |
https://www.mdpi.com/2227-7390/8/3/422 |
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