Symmetries in nonlinear control systems

A concept of symmetry is defined for general nonlinear control systems. It is shown, under various technical conditions, that nonlinear control systems with symmetries admit local and/or global decompositions in terms of lower dimensional subsystems and feedback loops. The structure of the individual subsystems is dependent on the structure of the symmetry group; for example, if the symmetry group is abelian, one of the subsystems is a quadrature. An additional feature of the decomposition is that the state space dimensions of the subsystems sum to the state space dimension of the original system.