Finite-Time and Fixed-Time Synchronization of Complex Networks with Discontinuous Nodes via Quantized Control

This paper investigates finite-time (FET) and fixed-time (FDT) synchronization of discontinuous complex networks (CNs) via quantized controllers. These control schemes can take full advantage of limited communication resources. By designing Lyapunov function and using different control schemes, several sufficient conditions are proposed such that the dynamical CNs are able to realize synchronization within a settling time. The settling time is related to the initial values of the considered systems using FET control, while it is regardless of the initial values when a special case of FET control named FDT control is utilized. Moreover, FET and FDT synchronization of discontinuous CNs are also considered via some existing controllers without logarithmic quantization, respectively. Numerical simulations are presented to demonstrate the theoretical results.