Journal
NEURAL NETWORKS
Volume 94, Issue -, Pages 76-85Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2017.06.012
Keywords
Fractional-order systems; Memristor-based neural networks; Stability; Synchronization; Multiple delays
Funding
- National Natural Science Funds of China [61403115, 11571016, 51607051, 51577046]
- State Key Program of National Natural Science Foundation of China [51637004]
- National Key Research and Development Plan 'important scientific instruments and equipment development' [2016YFF0102200]
- Natural Science Foundation of Anhui Province [1508085QF120]
- Fundamental Research Funds for the Central Universities [JZ2016HGTB0718, JZ2016HGXJ0022]
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The paper presents theoretical results on the global asymptotic stability and synchronization of a class of fractional-order memristor-based neural networks (FMNN) with multiple delays. First, the asymptotic stability of fractional-order (FO) linear systems with single or multiple delays is discussed. Delay-independent stability criteria for the two types of systems are established by using the maximum modulus principle and the spectral radii of matrices. Second, new testable algebraic criteria for ensuring the existence and global asymptotic stability of the system equilibrium point are obtained by employing the Kakutani's fixed point theorem of set-valued maps, the comparison theorem, and the stability criterion for FO linear systems with multiple delays. Third, the synchronization criterion for FMNN is presented based on the linear error feedback control. Finally, numerical examples are given demonstrating the effectiveness of the proposed results. (C) 2017 Elsevier Ltd. All rights reserved.
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