Time-synchronized control with the least upper bound of fixed settling time

This paper introduces time-synchronized convergence in fixed-time control, where all system states converge to the origin at the same time before a fixed time instant. Sufficient Lyapunov conditions are derived for fixed-time synchronized control (FTSC). An enhanced estimation method for synchronized settling time (ST) is proposed, with an explicit formula for its least upper bound (LUB), which reduces overestimation compared to existing methods. A switching-based technique is incorporated into the controller to avoid singularities while maintaining compatibility with the time-synchronized design. Simulation results validate the fixed-time synchronization properties and the improved ST estimation, demonstrating smoother output trajectories and reduced energy consumption.