Variable structure systems nonlinear in the control law

The most relevant results of Utkin's work obtained for variable structure systems linear in the control law which slide on suitable manifolds in the state space, are extended to some class of fully nonlinear plants. The equivalence between the Filippov solution concept is proved for this class. Further, the approximability property (convergence to the nonideal sliding motion to the ideal) is shown to hold for an important subclass.