Open AccessQuasi‐synchronisation of fractional‐order memristor‐based neural networks with parameter mismatches
Author(s) -
Huang Xia,
Fan Yingjie,
Jia Jia,
Wang Zhen,
Li Yuxia
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0196
Subject(s) - lemma (botany) , memristor , control theory (sociology) , differential inclusion , artificial neural network , mathematics , function (biology) , set (abstract data type) , lyapunov function , state (computer science) , upper and lower bounds , computer science , mathematical optimization , control (management) , algorithm , nonlinear system , artificial intelligence , engineering , ecology , mathematical analysis , physics , poaceae , electrical engineering , quantum mechanics , evolutionary biology , biology , programming language
This study addresses the problem of quasi‐synchronisation of fractional‐order memristor‐based neural networks (FMNNs) with time delay in the presence of parameter mismatches. Under the framework of fractional‐order differential inclusions and set‐valued maps, quasi‐synchronisation of delayed FMNNs is discussed and quasi‐synchronisation criteria are established by means of constructing suitable Lyapunov function, together with introducing some fractional‐order differential inequalities. A new lemma on the estimate of Mittag–Leffler function is derived first, which extends the application of Mittag–Leffler function and plays a key role in the estimate of synchronisation error bound. Then, linear state feedback combined with delayed state feedback control law is designed, which guarantees that for a predetermined synchronisation error bound, quasi‐synchronisation of two FMNNs with mismatched parameters will be achieved provided that the feedback gains satisfy the newly‐proposed criteria. The obtained results extend and improve some previous published works on synchronisation of FMNNs. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.