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.
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 [10.1109/TAC.2002.808465].
Solving quadratic distance problems: an LMI based approach
CHESI, GRAZIANO;GARULLI, ANDREA;VICINO, ANTONIO
2003-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/26729
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