Robustness Analysis of a Set of Second Order Sliding Modes

Abstract

In this paper, a set of second order sliding mode controllers affected by disturbances with linear and nonlinear growth is under study. Mechanical systems described using a double integrator affected by external perturbations are considered in this work. A preliminary study shows that, using a nonsmooth strict Lyapunov function, it is possible to ensure finite-time stability and estimate the convergence time of the closed loop system in spite of disturbances that grow linearly and nonlinearity with respect to the state. The performance and robustness properties of the feedback synthesis are illustrated with numerical experiments solving the tracking problem for a one-link pendulum as a test system. Three experiments are carried out: the nominal system, the system affected by nonvanishing perturbations and the system affected by linearly and nonlinearity growing perturbations with respect to the state.