An LMI approach to nonlinear sliding surface design

The problem of designing a nonlinear sliding surface for an uncertain system is considered. The proposed sliding surface comprises a linear time invariant term and an additional time varying nonlinear term. It is assumed that a linear sliding surface parameter matrix guaranteeing the asymptotic stability of the sliding mode dynamics is given. The linear sliding surface parameter matrix is used for the linear term of the proposed sliding surface. The additional nonlinear term is designed so that a Lyapunov function decreases more rapidly. By including the additional nonlinear term to the linear sliding surface parameter matrix we obtain a nonlinear sliding surface such that the speed of responses is improved. We also give a switching feedback control law inducing a stable sliding motion in finite time. Finally, we give an LMI-based design algorithm, together with a design example.