Journal
AUTOMATICA
Volume 40, Issue 1, Pages 21-35Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2003.08.001
Keywords
affine systems; piecewise-linear systems; polytope; facet; reachability; control law
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Given an affine system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-affine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to affine systems on full-dimensional simplices. In this case, the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law, that solves the reachability problem under consideration. (C) 2003 Elsevier Ltd. All rights reserved.
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