Robust tracking of perturbed nonlinear systems by nested sliding mode control

In this paper, we consider nested sliding mode control of SISO nonlinear systems to track a reference signal. The proposed system is perturbed by bounded matched and unmatched uncertainties and assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output tracks the desired exogenous system output, while the system states are forced arbitrary close to the intersection of sliding surfaces and remain bounded.