access icon free Quasi-synchronisation of fractional-order memristor-based neural networks with parameter mismatches

© The Institution of Engineering and Technology
Received 17/02/2017, Accepted 26/05/2017, Revised 28/04/2017, Published 30/05/2017

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.

Inspec keywords: neural chips; control system synthesis; state feedback; synchronisation; neurocontrollers; delay systems; Lyapunov methods; linear systems; memristor circuits

Other keywords: fractional-order differential inequalities; synchronisation error bound estimation; delayed FMNNs; linear state feedback; Mittag–Leffler function; parameter mismatches; Lyapunov function; fractional-order differential inclusions; quasisynchronisation criteria; delayed state feedback control law design; fractional-order memristor-based neural networks; set-valued maps; time delay

Subjects: Linear control systems; Distributed parameter control systems; Neurocontrol; Stability in control theory; Control system analysis and synthesis methods; Neural nets (circuit implementations)

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