Adaptive integral-type sliding mode control for a class of uncertain nonlinear systems

An integral-type sliding mode control method for a class of uncertain nonlinear systems in parameter feedback form is developed. The design procedure can be divided into two steps. Firstly, design a nonlinear integral-type sliding manifold for the uncertain system such that not only the sliding motion can occur on that manifold, but also the system´s motion along the manifold is asymptotically stable. The integral-type sliding surface is constructed by adding an integral term into the linear sliding surface. The additional integral in the proposed sliding surface provides one more degree of freedom; Secondly, based on the Lyapunov stability theorem, design a control law, such that the system´s states are driven towards the manifold and stay there for all future time, regardless of uncertainties.