Fixed-time synchronization criteria for complex networks via quantized pinning control

In this paper, fixed-time (FDT) synchronization of complex networks (CNs) is considered via quantized pinning controllers (QPCs). New control schemes with logarithmic quantization are designed, which not only can reduce control cost but also can save channel resources. The QPC with sign function can be used more generally than the QPC without sign function, but the QPC without sign function can be utilized to overcome the chattering phenomenon in some existing results. Based on designed Lyapunov function and different control schemes, several FDT synchronization criteria expressed by linear matrix inequalities (LMIs) are presented. Moreover, a numerical example is presented to illustrate the theoretical results.