R. Sepulchre et D. Aeyels, STABILIZABILITY DOES NOT IMPLY HOMOGENEOUS STABILIZABILITY FOR CONTROLLABLE HOMOGENEOUS SYSTEMS, SIAM journal on control and optimization, 34(5), 1996, pp. 1798-1813
This paper presents an example of a homogeneous planar controllable sy
stem which is stabilizable while not stabilizable by homogeneous feedb
ack. Addition of an integrator to the system provides a three-dimensio
nal affine system with the same properties.