Quadratic stabilization of bilinear control systems

In this paper, the problem of stabilization of bilinear control systems is considered. Based on the technique of linear matrix inequalities and quadratic Lyapunov function, the so-called stabilizability ellipsoid is designed, such that the trajectory of the closed-loop system, starting inside the ellipsoid asymptotically tends to zero. The results obtained allow to design an approximation of the stabilizability domain of the bilinear control system.