Ryan, E. P. On Brockett’s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback. (English) Zbl 0806.93049 SIAM J. Control Optimization 32, No. 6, 1597-1604 (1994). 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) Cited in 39 Documents MSC: 93D15 Stabilization of systems by feedback 55M25 Degree, winding number 93B52 Feedback control 34D99 Stability theory for ordinary differential equations Keywords:smooth feedback; discontinuous feedback Citations:Zbl 0528.93051 PDFBibTeX XMLCite \textit{E. P. Ryan}, SIAM J. Control Optim. 32, No. 6, 1597--1604 (1994; Zbl 0806.93049) Full Text: DOI