Nonlinear feedback control of a class of on-off control systems: An approach based on analytical solution of PDE’s

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 thrusters. A sufficient condition for global stability is derived, which is characterised by partial differential inequality about the state feedback laws. Further, it is shown that the feedback laws can be obtained analytically via solving some PDE´s and a class of control laws parameterized by a nonlinear function is shown explicitly.