# Chain-Scattering Approach to H^{∞} Control

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Part of the Systems & Control: Foundations & Applications book series (SCFA)

The advent of H-infinity-control was a truly remarkable innovation in multivariable theory. It eliminated the classical/modern dichotomy that had been a major source of the long-standing skepticism about the applicability of modern control theory, by amalgamating the "philosophy" of classical design with "computation" based on the state-space problem setting. It enhanced the application by deepening the theory mathematically and logically, not by weakening it as was done by the reformers of modern control theory in the early 1970s.

However, very few practical design engineers are familiar with the theory, even though several theoretical frameworks have been proposed, namely interpolation theory, matrix dilation, differential games, approximation theory, linear matrix inequalities, etc. But none of these frameworks have proved to be a natural, simple, and comprehensive exposition of H-infinity-control theory that is accessible to practical engineers and demonstrably the most natural control strategy to achieve the control objectives.

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-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 chain-scattering 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 conpletely self contained and requires little mathematical background other than some familiarity with linear algebra. It will be useful to praciticing engineers in control system design and as a text for a graduate course in H-infinity-control and its applications.

*The reader is supposed to be acquainted with linear systems only at an elementary level and, although full proofs are given, the exposition is careful so that it may be accessible to engineers. H. Kimura's textbook is a useful source of information for everybody who wants to learn this part of the modern control theory in a thorough manner. *—**Mathematica Bohemica**

*The book is useful to practicing engineers in control system design and as a textbook for a graduate course in H∞ control and its applications. *—**Zentralblatt MATH**

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- DOI https://doi.org/10.1007/978-1-4612-4080-8
- Copyright Information Birkhäuser Boston 1997
- Publisher Name Birkhäuser Boston
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4612-8642-4
- Online ISBN 978-1-4612-4080-8
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