This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.

This paper is concerned with quasi-synchronization of delayed memristive neural networks (MNNs) with switching jumps mismatches via aperiodically intermittent control. The issue is presented for three reasons: 1) the existing controllers for synchronization may be too complicated and not economical; 2) under the influence of switching jumps mismatches, synchronization of MNNs may fail to achieve; and 3) matrix measure method is less conservative but cannot be applied directly to synchronization of MNNs. To overcome these difficulties, the concept of asynchronously switching time interval is proposed to describe the phenomenon when the drive-response MNNs switch their connection weights asynchronously. Then, aperiodically intermittent control is designed and quasi-synchronization analysis is carried out based on a combined method that compromises the merits of interval matrix method and matrix measure method. A quasi-synchronization criterion, expressed in terms of the mixture of p-norm and matrix measure of the memristive connection weights, is established. Meanwhile, the fundamental reason for the failure of complete synchronization is revealed. Moreover, an explicit expression of the error level is obtained and the design of the controller under a predetermined error level is presented. The obtained results in this paper reduce the conservativeness and provide a novel insight into the research of synchronization of MNNs.

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.