Discontinuous Control of the Brockett Integrator

The problem of asymptotic stabilisation of the Brockett integrator has been addressed and solved in recent years with a variety of methods and approaches. In particular, several discontinuous control laws guaranteeing exponential convergence in an open and dense set have been proposed. In this work We show that all such discontinuous controllers can be obtained as special cases of a more general class of controllers. Furthermore, the problem of stabilisation with bounded control is also discussed and solved. Finally, we address the problem of controlling the kinematic model of an under-actuated satellite. Simulation results complete the work.