Abstract
Realization of nonlinear systems by state-space is a classical problem in control theory. This problem has been completely solved by Kaiman [10] in the case of linear systems. Similarly, it was solved for bilinear systems (see Brockett [2], d’Alessandro, Isidori, Ruberti [1], Fliess [3], Sussmann [12]). In the general case, let us mention the work of Sussmann [13], Hermann, Krener [7] and Jakubczyk [9]: 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 [5].
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References
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© 1986 D. Reidel Publishing Company
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Reutenauer, C. (1986). The Local Realization of Generating Series of Finite Lie Rank. In: Fliess, M., Hazewinkel, M. (eds) Algebraic and Geometric Methods in Nonlinear Control Theory. Mathematics and Its Applications, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4706-1_2
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DOI: https://doi.org/10.1007/978-94-009-4706-1_2
Publisher Name: Springer, Dordrecht
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