Linear Matrix Inequalities (LMIs) have emerged as useful tools for solving a number of control problems. This volume provides an account of LMI method and covers topics such as LMI algorithms, analysis and synthetic issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control. The basic idea of the LMI method in control is to approximate a given control problem via an optimization problem with linear objective and so-called LMI constants. The LMI method leads to an efficient numerical solution and is particularly suited to problems with uncertain data and multiple (possibly conflicting) specifications.