We consider new results related to control design problem for continuous-time bilinear systems subjected to arbitrary иounded exogenous disturbances. A simple procedure for the construction of the ellipsoid of stabilizability and the domain of stabilizability for bilinear control systems is proposed and its efficiency is proved. The main tools are the quadratic Lyapunov functions and the linear matrix inequality technique. This simple but general approach has great potential and can be widely generalized; for instance, to various robust statements of the problem.