Global second-order sliding mode control for nonlinear uncertain systems

Abstract

Second-order sliding mode (SOSM) control is used to keep exactly a constraint σ of the second relative degree or to avoid chattering phenomenon. Yet, the traditional SOSM controllers are designed based upon the assumption that the uncertainties or their derivatives are bounded by positive constants. In this paper, a global SOSM controller is designed for a general class of single-input–single-output nonlinear systems with uncertainties bounded by positive functions. Moreover, a variable-gain robust exact differentiator is developed such that the SOSM controllers with finite-time convergence can also be implemented even when the derivative of the constraint σ is unavailable. Simulation results are given to show the effectiveness of the proposed method.