Quadratic stabilization of bilinear control systems

In this paper, a stabilization problem of bilinear control systems is considered. Using the linear matrix inequality technique and quadratic Lyapunov functions, an approach is proposed to the construction of the so-called stabilizability ellipsoid such that the trajectories of the closed-loop system emanating from any point inside this ellipsoid asymptotically tend to the origin. The approach allows for an efficient construction of nonconvex approximations to stabilizability domains of bilinear systems.
The results are extended to robust formulations of the problem, where the system matrix is subjected to structured uncertainty.