The problem of invariant output tracking is considered: given a control system
admitting a symmetry group G, design a feedback such that the
closed-loop system tracks a desired output reference and is invariant under the action of G.
Invariant output errors are defined as a set
of scalar invariants of G; they are calculated with the Cartan moving frame
method. It is shown that standard tracking methods based on input-output linearization can be applied to
these invariant errors to yield the required “symmetry-preserving” feedback
