Jorge Cortés
Professor
Vectorvalued quadratic forms in control theory
F. Bullo, J. Cortés, A.D. Lewis, S. Martínez
Unsolved Problems in Mathematical Systems and Control Theory,
eds. V. Blondel and A. Megretski, Princeton University Press, 2004,
pp. 315320
Abstract
Given two real vector spaces U and V, and a symmetric bilinear map B:
U x U > V, let Q_B be its associated quadratic map. The problems we
consider are as follows: (i) are there necessary and sufficient
conditions, checkable in polynomialtime, for determining when Q_B is
surjective?; (ii) if Q_B is surjective, given v belonging to V is
there a polynomialtime algorithm for finding a point u in the inverse
image of v by Q_B?; (iii) are there necessary and sufficient
conditions, checkable in polynomialtime, for determining when B is
indefinite? We present an alternative formulation of the problem of
determining the image of a vectorvalued quadratic form in terms of
the unprojectivised Veronese surface. The relation of these questions
with several interesting problems in Control Theory is illustrated.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 920930411
Ph: 18588227930
Fax: 18588223107
cortes at ucsd.edu
Skype id:
jorgilliyo