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A canonical expansion for nonlinear systems

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2 Author(s)
Renjeng Su ; University of Colorado, Boulder, CO, USA ; Hunt, L.

The importance of differential geometry, in particular, Lie brackets of vector fields, in the study of nonlinear systems is well established. Under very mild assumptions, we show that a real-analytic nonlinear system has an expansion in which the coefficients are computed in terms of Lie brackets. This expansion occurs in a special coordinate system. We also explain the concept of a pure feedback system. For control design involving a nonlinear system, one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths.

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Automatic Control, IEEE Transactions on  (Volume:31 ,  Issue: 7 )