Complete synchronization in predetermined/fixed-time for multilayered networks under edge-based discontinuous control

Abstract

Achieving synchronization in a designated time for multilayered networks (MLNs) is particularly challenging when state information is unavailable. This study provides theoretical solutions to the fixed-time (FIM) and predetermined-time (PIM) synchronization problems in MLNs. Firstly, a high-resolution model of MLNs is established with both intra-layer and inter-layer coupling. Additionally, a practical PIM stability theorem and high-precision settling time estimation are formulated. Furthermore, two edge-based event-triggered intermittent control (EAIC) strategies are developed for MLNs using various auxiliary functions. FIM/PIM synchronization issues are addressed while eliminating Zeno behaviors throughout, except during the settling time. Ultimately, the feasibility of the proposed theory is demonstrated through the design of a synchronization circuit within the complex system.