Every convex free basic semi-algebraic set has an LMI representation

Abstract

The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex free basic open semi-algebraic set. The main theorem of this paper is a converse, each such set arises from some LMI. The result has implications for semi-definite programming and systems engineering as well as for free semi-algebraic geometry.

Authors

J. William Helton

Department of Mathematics, University of California San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093-0112

Scott McCullough

Department of Mathematics, University of Florida, 490 Little Hall, Gainesville, FL 32611-8105