期刊
AUTOMATICA
卷 40, 期 5, 页码 773-787出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2004.01.001
关键词
uncertain linear equations; set-valued filtering; interior-point methods; bounding ellipsoids; linear matrix inequalities (LMI); structured and parametric uncertainty; linear fractional transformation
In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the J-procedure. This formulation leads to convex optimization problems that can be essentially solved in O(n(3))-n being the size of unknown vector-by means of suitable interior point barrier methods, as well as to closed form results in some particular cases. We further show that the uncertain linear equations paradigm can be directly applied to various state-bounding problems for dynamical systems subject to set-valued noise and model uncertainty. (C) 2003 Elsevier Ltd. All rights reserved.
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