Optimization of bilinear control systems subjected to exogenous disturbances. II. Design

We obtain and discuss new results related to control design for bilinear systems subjected to arbitrary bounded exogenous disturbances. A procedure for the construction of the stabilizability ellipsoid and the domain of stabilizability for bilinear control 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 and can be widely generalized; for instance, to various robust statements of the problem.