Nonlinear systems, the associated angular system and stabilisation

The stabilizability of a general class of nonlinear systems is studied by considering the associated angular system, which leads to a simple stabilizing controller in many cases. Examples including the case of bilinear systems are presented in both finite- and infinite-dimensional cases. The method consists of writing the system in the form of a nonlinear equation on a sphere and a radial differential system- the latter is easily controlled under certain conditions on the control vector field.