Nonsingular Fixed-time Sliding Mode Control for Second-order Systems with Unknown Disturbance

This paper peruses the finite/fixed-time stability problem of classical second order systems with unknown external disturbance. Based on the sliding mode control approach, a finite-time controller is first proposed to achieve the stability of the closed-loop system. Then, to remove the limitation of convergence rate relying on initial states, a novel fixed-time controller is further proposed. It is noteworthy that both the two controllers are globally effective. Moreover, to solve the singularity problem of the terminal sliding mode approach, a novel method of singular area division is introduced into the construction of the proposed switching controller. Thus, this treatment achieves finite/fixed-time convergence without singularity in both areas of phase plane, which offers more feasibility in practice. Finally, numerical simulation results are performed to verify the effectiveness of the proposed algorithms.