Solving quadratic distance problems: an LMI-based approach

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) techn...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2003-02, Vol.48 (2), p.200-212
Main Authors: Chesi, G., Garulli, A., Tesi, A., Vicino, A.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Computer science
control theory
systems
Computer simulation
Control system analysis
Control systems
Control theory. Systems
Exact sciences and technology
Linear matrix inequalities
Lower bounds
Mathematical models
Miscellaneous
Nonlinear control systems
Nonlinear systems
Numerical simulation
Optimization
Representations
Stability
Symmetric matrices
Testing
Tightness
Uncertainty
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2002.808465