Stabilization of bilinear systems via linear state feedback control

In this paper we consider the problem of stabilizing a bilinear system via linear state feedback control. A procedure is proposed which, given a polytope V surrounding the origin of the state space, finds, if existing, a controller in the form u = Kx, such that the zero equilibrium point of the closed loop system is asymptotically stable and V is enclosed into the domain of attraction of the equilibrium. The controller design requires the solution of a convex optimization problem involving linear matrix inequalities. An example illustrates the applicability of the proposed technique.