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Zbl 0806.93049
Ryan, E.P.
On Brockett's condition for smooth stabilizability and its necessity in a context of nonsmooth feedback. (English)
[J] SIAM J. Control Optimization 32, No.6, 1597-1604 (1994). ISSN 0363-0129; ISSN 1095-7138/e

{\it R. W. Brockett} [Differential geometric control theory, Proc. Conf., Mich. Technol. Univ. 1982, Prog. Math. 27, 181-191 (1983; Zbl 0528.93051)] presented a necessary condition for stabilizability of nonlinear systems by smooth feedback. The author shows that this condition persists to be necessary when the class of controls is enlarged to enclude discontinuous feedback. The proof is based on properties of a degree for set-valued maps.
[W.Müller (Berlin)]

MSC 2000:: *93D15 Stabilization of systems by feedback
55M25 Degree, etc.
93B52 Feedback control
34D99 Stability theory of ODE

Keywords: smooth feedback; discontinuous feedback

Citations: Zbl 0528.93051

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