Fixed-Time Synchronization of Spatiotemporal Networks via Quantized Boundary Control

In this paper, the fixed-time synchronization of spatiotemporal networks under quantized boundary control is investigated, where the network coupling encompasses both state coupling and spatial diffusion coupling. First, under the mixed boundary condition, two innovative power-law controllers embedded with a quantization mechanism are designed, and the controllers operate at the boundary of the spatial domain. Subsequently, by employing inequality techniques and fixed-time stability theory, several verifiable criteria are derived to ensure the fixed-time synchronization of the addressed spatiotemporal networks. Lastly, the theoretical results are validated through by numerical simulations of two illustrative examples.