Predefined‐time synchronization of memristor‐based bidirectional associative memory neural networks with time‐varying delays

Abstract In this paper, two novel and general predefined‐time stability (PTSt) lemmas are introduced and applied to address the predefined‐time synchronization (PTSy) problem in memristor‐based bidirectional associative memory (BAM) neural networks. Unlike traditional finite‐time synchronization (FinTS) or fixed‐time synchronization (FixTS) approaches, the synchronization time in this study is independent of the initial states (InSts) and system parameters. It can be predetermined according to task requirements without any estimation. Two effective and innovative controllers are designed to achieve synchronization in time‐delayed memristor‐based BAM neural networks (MBAMNNs) based on PTSt. The proposed controllers employ general PTSy analysis to ensure robust synchronization performance. These diverse predefined‐time controllers (PTCos) design facilitates the practical implementation of synchronization control in neural networks. By employing the fraction‐order power function and exponential function, the PTCos offer flexibility and adaptability in controller design. The results are validated through two numerical examples using MATLAB simulations.