Design of adaptive sliding surfaces for systems with mismatched perturbations to achieve asymptotical stability

On the basis of the Lyapunov stability theorem, a design of adaptive sliding surfaces for a class of MIMO systems with matched and mismatched perturbations is proposed to solve regulation problems. By utilising some adaptive gains designed both in the sliding surface function and in the controllers, not only are the mismatched perturbations automatically overcome during the sliding mode, but the property of asymptotical stability of controlled systems is also achieved at the same time. Furthermore, the knowledge of the upperbound of partial perturbations is not required. A numerical example is given to demonstrate the feasibility of the proposed control scheme.