Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks.

Abstract

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0<Vt⩽1 are no longer required. For the purpose of verifying the new lemmas, complex-valued fuzzy cellular neural networks (CVFCNNs) with discontinuous activation functions are studied with a nontraditional non-separation method, which could reduce the conservatism of the obtained results greatly. Besides, FXT synchronization is discussed simultaneously. When contrasted with the results of other similar prominent pioneering works nowadays, the accuracy of settling times (STs) is quite enhanced. At last, numerical simulations are conducted to demonstrate the validity and superiority of our established theoretical results.