From Local to Global Feedback Controllers: A Symmetry‐Based Approach

We introduce a novel procedure for designing global state- or output-feedback controllers for ordinary differential nonlinear systems (ODE) from the knowledge of a local state- or output-feedback controller and a symmetry of the system. Symmetries are one-parameter transformations which leave invariant the structure of the system by mapping solutions into other (parametrized) solutions. We use particular types of symmetry, called contracting symmetry, which uniformly contract solutions into arbitrary small solutions around the origin. This contracting action allows to obtain global feedback controllers from local feedback controller by inverse transformation via the symmetry.