LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems

We propose a linear matrix inequality (LMI)-based sliding surface design method for integral sliding-mode control of mismatched uncertain systems. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix as well as the input matrix. We give a sufficient condition for the existence of a sliding surface guaranteeing asymptotic stability of the full order sliding mode dynamics. We also give an LMI characterization of the sliding surface, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Additionally, we give an LMI condition of sliding surfaces guaranteeing the alpha-stability constraint. Finally, we give a simulation result to show the effectiveness of our method