Continuous robust fixed-time control for double integrator system with matched disturbance

This paper investigates the continuous robust fixed-time control for the double integrator system with matched disturbance. A new integral-type sliding mode (ISM) fixed-time controller is proposed that can significantly alleviate the chattering phenomenon and ensure the states of double integrator system to converge to the origin within a fixed settling time. Continuous Lyapunov functions are given and a valid proof for the closed loop system is presented based on the bi-limit homogeneous theorem. An output feedback ISM fixed-time controller is also developed for the disturbed double integrator system based on a fixed-time observer. Numerical simulations are provided to demonstrate the performance of proposed continuous robust fixed-time algorithms.