A New Predefined Time Stability Theorem and its Application in Multi-Modal Memristive Neural Network Synchronization

This article proposes a new predefined-time (PDT) stability theorem, which offers more evident advantages compared to previous predefined-time stability. Firstly, based on the limitations of existing PDT stability, this theorem relaxed the limitations of sufficient conditions, which fill the gap in the research on PDT stability. Secondly, the PDT synchronization of multi-modal memristive neural networks (MM-MNN) is analyzed by the usability of the new judgment theorem. A matching PDT controller is designed and sufficient synchronization control conditions is obtained by utilizing generalized Lyapunov functional method, set-valued mapping, inequality analysis technique and differential inclusion theory. Meanwhile, the topological characteristics of multi-modal neuron and its impact on network synchronization behavior are presented. Finally, we provide some confirmatory numerical simulations.