A new judgment theorem for predefined‐time stability and its application in the synchronization analysis of neural networks

Abstract

AbstractCompared with finite‐time/fixed‐time stability, predefined‐time (PDT) stability has some obvious advantages, so it is expected to be the next hot topic. The study of PDT stability depends heavily on the judgment theorems for PDT stability. However, all the existing judgment theorems for PDT stability have several drawbacks, such as complicated judging conditions and strict parameter selection. In this article, a new judgment theorem for PDT stability is proposed to fill the gap, and it is based on a very concise judging condition. To verify the usability of the new judgment theorem, we devise a matching PDT controller, and analyze the PDT synchronization of neural networks by means of the novel judgment theorem. We derive several PDT synchronization criteria, which guarantee the considered neural networks can reach PDT synchronization within an arbitrary preassigned time. The preassigned time can be set as a specific parameter in the devised controller, and the other controller parameters can also be selected easily. Lastly, we provide some confirmatory numerical simulations.