  This paper is motivated by the problem of asymptotically stabilizing
invariant sets in the state space of control systems by means of output
feedback. The sets considered are smooth embedded in submanifolds and the class
of system is nonlinear, finite-dimensional, autonomous, deterministic,
single-input and control-affine. Given an invariant set and a control system
with fixed output, necessary and sufficient conditions are presented for
feedback equivalence to a normal form that facilities the design of output
feedback controllers that stabilize the set using existing design techniques.
