Time-Compensation Locally Fixed-Time Stabilization of First-Order Systems With Input Saturation

Abstract

This letter proposes a structurally simple, locally fixed-time stabilization method for first-order systems with input saturation by introducing a time-compensation coefficient. Unlike conventional anti-saturation compensation approaches, the proposed controller preserves the nominal fixed-time control structure while ensuring convergence within a bounded time independent of initial conditions. The key innovation lies in direct adaptation of the time-compensation coefficient, which is determined by using the relationship between the Lyapunov function and the convergence time of fixed-time stable system. Theoretical analysis confirms local fixed-time stability under input saturation, with the upper bound of the convergence time not changed. This method also shows the potential to be applied to high-order systems. Numerical simulations on a first-order system demonstrate that the proposed controller achieves the original convergence time despite saturation.