This book is the first comprehensive treatment of the "fractional representation" approach to linear feedback system design and analysis, an approach that has recently taken the control theory field by storm. It unfolds several basic themes, virtually all of which are new and which are destined to play a fundamental role in algebraic system theory in years to come. It offers a very basic introduction to the factorization method for scalar systems and a thorough treatment of coprime factorizations including H∞ theory. Contents:Introduction; Proper Stable Rational Functions; Scalar Systems: An Introduction; Matrix Rings; Stabilization; Filtering and Sensitivity Minimization; Robustness; Extensions to General Settings; Appendixes: Algebraic Preliminaries, Preliminaries on Matrix Rings, Topological Preliminaries; References and Index. Mathukumalli Vidyasagar is Professor of Electrical Engineering, University of Waterloo, Ontario, Canada. Control System Synthesisis seventh in the MIT Press Signal Processing, Optimization, and Control Series, edited by Alan S. Willsky.