THE PROJECTIVE METHOD FOR SOLVING LINEAR MATRIX INEQUALITIES

Numerous problems in control and systems theory can be formulated in t erms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be n umerically tractable. However, the interest in LMI-based design techni ques has really surged with the introduction of efficient interior-poi nt methods for solving LMIs with a polynomial-time complexity, This pa per describes one particular method called the Projective Method. Simp le geometrical arguments are used to clarify the strategy and converge nce mechanism of the Projective algorithm. A complexity analysis is pr ovided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed. (C) 1997 The Mathematica l Programming Society, Inc. Published by Elsevier Science B.V.