Aperiodically Intermittent Control for Quasi-Synchronization of Delayed Memristive Neural Networks: An Interval Matrix and Matrix Measure Combined Method

Abstract

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.