Robust nonlinear state-feedback control of second-order systems (2406.14000v2)

Abstract: This note proposes a novel nonlinear state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output state of interest and its time derivative, while achieving robust control in a finite time. The control has only one free design parameter, and the closed-loop system is shown to be uniformly asymptotically stable in the presence of matched disturbances. We derive a strict Lyapunov function for the closed-loop control system with a bounded exogenous perturbation, and use it for both the control parameter tuning and analysis of the finite-time convergence. Apart from the numerical results, a revealing experimental example is also shown in favor of the proposed control and in comparison with PD and sub-optimal nonlinear damping regulators.