Robust Tracking of a Class of Perturbed Nonlinear Systems via Multivariable Nested Sliding Mode Control

Abstract

In this paper, a new methodology for robust controller design in nonlinear multivariable systems is suggested to guarantee asymptotic output tracking. The systems under consideration are perturbed by functionally bounded matched and unmatched uncertainties/perturbations and assumed to be described in the strict-feedback form. The main idea of the methodology is based on the combination of conventional sliding mode control and backstepping algorithm. The proposed controller called nested sliding mode controller that is obtained through a stepwise algorithm. It has the ability of rejecting nonvanishing perturbations by using dynamic switches, unlike conventional and other hierarchical sliding mode design methods. Performance is studied through theorems and verified by two numerical examples.