Robust finite-time output feedback control of perturbed double integrator

This paper addresses the problem of finite-time output feedback stabilization for the perturbed double integrator system. A simple output feedback proportional–derivative (PD) controller is proposed. Global finite-time stability is proven based on Lyapunov stability theory and geometric homogeneity technique. Furthermore, it is proven that the proposed controller can maintain local finite-time stability regardless of some nonlinear perturbations. Thus, the proposed controller actually can be applied to a large class of uncertain second-order nonlinear systems. Simulations demonstrate the effectiveness of the proposed approach.