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We construct discontinuous feedback laws, and particularly we make it possible to choose these continuous outside a small set (closed with measure zero) of discontinuity in the case of control systems which are affine in the control; moreover this set of singularities is shown to be repulsive for the Carath\u00e9odory solutions of the closed-loop system under an additional assumption.<\/jats:p>","DOI":"10.1137\/s0363012900375342","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"659-681","source":"Crossref","is-referenced-by-count":82,"title":["Semiconcave Control-Lyapunov Functions and Stabilizing Feedbacks"],"prefix":"10.1137","volume":"41","author":[{"given":"Ludovic","family":"Rifford","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02567770"},{"key":"R2","first-page":"3","volume":"6","author":"Alexandroff A.","year":"1939","journal-title":"Leningrad State Univ. 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