The purpose of this book is to provide such a natural theoretical framework that is understandable with little mathematical background. The notion of chain-scattering, well known in classical circuit theory, but new to control theorists, plays a fundamental role in this book. It captures an essential feature of the control systems design, reducing it to a J-lossless factorization, which leads us naturally to the idea of H[superscript infinity]-control.

The J-lossless conjugation, an essentially new notion in linear system theory, then provides a powerful tool for computing this factorization. Thus the chainscattering representation, the J-lossless factorization, and the J-lossless conjugation are the three key notions that provide the thread of development in this book. The book is completely self contained and requires little mathematical background other than some familiarity with linear algebra.

It will be useful to practicing engineers in control system design and as a text for a graduate course in H[superscript infinity]-control and its applications.