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The structure of nonlinear control systems possessing symmetries

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2 Author(s)
Grizzle, J.W. ; University of Illinois, Urbana, IL, USA ; Marcus, S.I.

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.

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Automatic Control, IEEE Transactions on  (Volume:30 ,  Issue: 3 )