The Local Realization of Generating Series of Finite Lie Rank
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Realization of nonlinear systems by state-space is a classical problem in control theory. This problem has been completely solved by Kaiman  in the case of linear systems. Similarly, it was solved for bilinear systems (see Brockett , d’Alessandro, Isidori, Ruberti , Fliess , Sussmann ). In the general case, let us mention the work of Sussmann , Hermann, Krener  and Jakubczyk : they assume that the solutions are regular at any time and for any inputs. This restriction lead Fliess to study local realization of nonlinear systems .
KeywordsConstant Term Left Ideal Formal Power Series Formal Series Convergent Series
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