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