Stabilization of two-dimensional single-input bilinear systems with a finite number of constant feedback controllers

In this paper, we consider the control problem of stabilizing a class of two-dimensional bilinear systems with a finite number of constant feedback controllers along with appropriate switchings. We show that the bilinear systems under consideration are stabilizable either by one constant feedback controller, or by two such controllers, or that they are not stabilizable by a finite number of such controllers.