Stabilization of a class of on-off control systems by nonlinear state feedback

This paper studies the feedback control of a class of linear systems actuated by on-off input. This class of systems includes many important applications such as the orientation control of satellites which are actuated by thrustors. A sufficient condition for global stability is derived, which is characterised by partial differential matrix inequality about the state feedback law. Further, it is shown that the feedback law can be obtained analytically via solving some PDE´s and a class of control laws parameterized by a nonlinear function is given explicitly.