We consider analysis problems for bilinear systems subjected to arbitrary bounded exogenous disturbances. A procedure for the construction of the stabilizability ellipsoid and domain of stabilizability for quadratic dynamical systems is proposed and its efficiency is proved. This problem is solved both in continuous and discrete time. The main tool is the linear matrix inequality technique. This simple yet general approach is of great potential; for instance, it can be generalized to various robust statements of the problem.