Sliding surface design for higher-ordersliding modes

Two main concepts for sliding surfaces design procedure: pole placement and optimal stabilization are generalized for the case of arbitrary order sliding modes. For the pole placement case, the formula of Ackermann-Utkin is extended allowing the design of sliding surfaces with arbitrary relative degree. The natural connection between order of singularity for singular optimal stabilization problem and order of sliding mode controller is shown and used in the design of the sliding surface and the sliding mode controller of corresponding order.