Fixed-Time Distributed Control for Networked Systems with High-Order Switching Dynamics via the FAS Method

This paper studies the fixed-time synchronization problem of networked systems with high-order switching nonlinear node dynamics. Firstly, the fully-actuated system (FAS) framework is employed to model and control the high-order nodes directly, thereby preserving the intrinsic dynamics and physical interpretability of the system. To analyze fixed-time stability of synchronization error system under switching behaviors, a switching accumulation (SA) function is introduced to characterize the cumulative effect of switching nonlinearities without requiring explicit dwell-time or average dwell-time assumptions. Based on the FAS formulation, a distributed switching fixed-time synchronization controller is developed for considered high-order complex networks, and explicit settling-time bounds independent of initial conditions are derived. Simulation results on a switching Kuramoto network verify the effectiveness of the proposed approach and illustrate a practical procedure for estimating the fixed settling time based on the SA function.