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Global transformations of nonlinear systems

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3 Author(s)
Hunt, L. ; Texas Tech University, Lubbock, TX, USA ; Renjeng Su ; Meyer, G.

Recent results have established necessary and sufficient conditions for a nonlinear system of the form \dot{x}(t) = f(x(t))-u(t)g(x(t)) . with f(0) = 0 , to be locally equivalent in a neighborhood of the origin in Rnto a controllable linear system. We combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system. In doing so we introduce a technique for constructing a transformation under the assumptions that \{g.[f.g],\cdots ,(ad^{n-1}f.g)\ span an n -dimensional space and that \{g.[f.g],\cdots ,(ad^{n-2}f.g)\ is an involutive set.

Published in:

Automatic Control, IEEE Transactions on  (Volume:28 ,  Issue: 1 )