Nonlinear, integral-type sliding surface for both matched and unmatched uncertain systems

This note presents a new nonlinear integral-type sliding surface which incorporates a virtual nonlinear nominal control to achieve prescribed specifications. First, the plant with matched uncertainties is considered. The resultant closed-loop system during ideal sliding mode behaves exactly like the nominal plant under the nonlinear nominal control, which completely nullifies the matched uncertainties and consequently satisfies the prescribed specifications. Second, the stability analysis of the proposed sliding mode for the systems with unmatched uncertainties is performed to exploit the stability conditions. Numerical results demonstrate the validity of the proposed concept.