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On Brockett’s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback. (English) Zbl 0806.93049

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.
Reviewer: W.Müller (Berlin)

MSC:

93D15 Stabilization of systems by feedback
55M25 Degree, winding number
93B52 Feedback control
34D99 Stability theory for ordinary differential equations

Citations:

Zbl 0528.93051
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