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

This paper presents a new nonlinear integral-type sliding surface which incorporates a virtual nonlinear nominal control to achieve the prescribed specifications. First, the plant with matched uncertainties is considered. The resultant closed-loop system during ideal sliding mode behaves exactly like a nominal plant under the nonlinear nominal control, which completely nullifies the matched uncertainties and consequently satisfies the prescribed specifications. Next, the stability analysis of the proposed sliding mode for the systems with unmatched uncertainties is performed to exploit the stability margin. Application examples to realize the eigenvalue assignment and linear quadratic regulator optimal control with respect to the linear part of a nominal plant are studied. Numerical results demonstrate the validity of the proposed scheme