The computation of the minimum distance of a point to a surface in a finite-dimensional space is a key issue in several system analysis and control problems. The paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality (LMI) techniques. Exploiting a suitable representation of homogeneous forms, a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one-parameter family of LMI optimization problems. Several properties of the proposed technique are discussed. In particular, tightness of the lower bound is investigated, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori. Extensive numerical simulations are reported showing promising performances of the proposed method.
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|Titolo:||Solving quadratic distance problems: an LMI based approach|
|Rivista:||IEEE TRANSACTIONS ON AUTOMATIC CONTROL|
|Citazione:||Chesi, G., Garulli, A., Tesi, A., & Vicino, A. (2003). Solving quadratic distance problems: an LMI based approach. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 48(2), 200-212.|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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