Abstract
This chapter begins by recalling basic results of nonlinear differential equations. Controllability and observability of nonlinear control systems are studied next. Two approaches to problems are illustrated: one based on linearization and the other one on concepts of differential geometry.
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Theorem 6.6 is due to E.B. Lee and L. Markus [63] and Theorem 6.9 to H.J. Sussmann and V. Jurdjevic [91]. The proof of Theorem 6.9 follows that of A.J. Krener [60]. Results of §6.4 and 6.5 are typical for geometric control theory based on differential geometry. More on this topic can be found in the monograph by A. Isidori [51]. Example 6.3 was introduced by R.W. Brockett [13].
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Zabczyk, J. (2020). Controllability and observability of nonlinear systems. In: Mathematical Control Theory. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-44778-6_6
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DOI: https://doi.org/10.1007/978-3-030-44778-6_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-44776-2
Online ISBN: 978-3-030-44778-6
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