Nested Continuous Sliding Mode Control for Matched and Unmatched Uncertainty Rejection in Nonlinear Systems

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