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Symmetries of nonlinear control systems in state representation areconsidered. To this end, a geometric approach to ordinary differentialequations is advocated. Invariant feedback laws for systems with Liesymmetries, i.e. feedback laws that preserve the symmetry group of a consideredplant, can be constructed based on invariants of the considered group action.Under minor technical assumptions suitable invariant tracking errors can bedetermined by following a normalization procedure. The underlying localgeometric meaning of this procedure is discussed and it is shown how it canalso be applied in order to derive a local, reduced-order systemrepresentation. Further, the idea of controlled symmetries, i.e. imposingdesired symmetry properties on a given control system by state feedback, isdiscussed by outlining an exemplary control design for a predator-preybioreactor.

On symmetries of nonlinear systems in state representation and application of invariant feedback design