Algorithms and software for LMI problems in control

A number of important problems from system and control theory can be numerically solved by reformulating them as convex optimization problems with linear matrix inequality (LMI) constraints. While numerous articles have appeared cataloging applications of LMIs to control system analysis and design, there have been few publications in the control literature describing the numerical solution of these optimization problems. The purpose of this article is to provide an overview of the state of the art of numerical algorithms for LMI problems, and of the available software.