Lyapunov-based Saturated Continuous Twisting Algorithm

In this article, a second-order system, which is affected by disturbances and
uncertainties, with a saturating actuator is considered. A novel robust feedback
control law is designed based on the sliding mode technique. The twisting and
the continuous twisting algorithms are incorporated into the design, which is
based on level curves of a Lyapunov function. The performance of the standard
continuous twisting algorithm is greatly improved in the case that the initial
condition of the system is far away from the origin. A parameter setting for the
controller is given by establishing global finite-time stability properties of the
closed-loop system origin. Feasibility and effectiveness of the proposed approach
are indicated in a real-world application as well as numerical simulation.