Quasi‐synchronisation of fractional‐order memristor‐based neural networks with parameter mismatches

Abstract

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.