Equivalence of sum of squares convex relaxations for quadratic distance problems
Article first published online: 2 APR 2012
Copyright © 2012 John Wiley & Sons, Ltd.
International Journal of Robust and Nonlinear Control
Volume 23, Issue 9, pages 965–977, June 2013
How to Cite
Garulli, A., Masi, A. and Vicino, A. (2013), Equivalence of sum of squares convex relaxations for quadratic distance problems. Int. J. Robust Nonlinear Control, 23: 965–977. doi: 10.1002/rnc.2810
- Issue published online: 24 APR 2013
- Article first published online: 2 APR 2012
- Manuscript Accepted: 12 FEB 2012
- Manuscript Revised: 15 JAN 2012
- Manuscript Received: 26 NOV 2010
- convex relaxations;
- SOS polynomials;
- robust control
This paper deals with convex relaxations for quadratic distance problems, a class of optimization problems relevant to several important topics in the analysis and synthesis of robust control systems. Some classes of convex relaxations are investigated using the sum of squares paradigm for the representation of positive polynomials. The main contribution is to show that two different relaxations, based respectively on the Positivstellensatz and on properties of homogeneous polynomial forms, are equivalent. Relationships among the considered relaxations are discussed and numerical comparisons are presented, highlighting their degree of conservatism. Copyright © 2012 John Wiley & Sons, Ltd.