Stabilization of Affine Systems with Control Singularities∗

This paper deals with the zero equilibrium stabilization problem for afine systems that have control input singularities. We consider a class of scalar input systems written in a canonical form with the input coeficient vanishing to zero on a set of points in the state space that includes the origin. The necessary and suficient conditions are obtained for the zero equilibrium stabilizability of such afine systems. As an example, stabilization of third-order dynamical systems by means of constant and variable state feedback controls is considered.