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.