In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems. Special Features: The book identifies a handful of standard optimization problems that are general (a wide variety of problems from system and control theory can be reduced to them) as well as specific (specialized numerical algorithms can be devised for them). Catalogues a diverse list of problems in system and control theory that can be reduced to the standard optimization problems. Problems considered are analysis and state feedback design for uncertain systems, matrix analysis problems, and many others. Most of the the book is accessible to anyone with a basic mathematics background, e.g., linear algebra and differential equations.