Continuous Twisting Algorithm

We propose a continuous homogeneous generalization of the Twisting Algorithm. The part of the algorithm ensuring the compensation of the perturbation has the structure of the Twisting algorithm so that we call it Continuous Twisting Algorithm (CTA). For a system with relative degree two and a Lipschitz perturbation CTA provides finite-time convergence to the origin for the output and its first derivative. Moreover, CTA also guarantees the finite-time convergence of the control signal to the uncertainties. The convergence is proved using a smooth strict homogeneous Lyapunov function. The positiveness of the proposed Lyapunov function and the negativeness of its derivative are verified using a method based on Pólya's Theorem.