| ## Linear Robust Control (Dover Books on Electrical Engineering) |

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## Book Description

After a brief introductory chapter, the text proceeds to examinations of multivariable frequency response design, signals and systems, and linear fractional transformations and their role in control systems. Subsequent chapters develop the control system synthesis theory, beginning with a concise treatment of the linear quadratic Gaussian problem and advancing to full-information H-infinity controller synthesis, the H-infinity filter, and the H-infinity generalized regulator problem. Concluding chapters examine model reduction by truncation, optimal model reduction, and the four-block problem. The text concludes with a pair of design case studies and helpful appendices. This treatment requires familiarity with linear algebra, matrix theory, linear differential equations, classical control theory, and linear systems theory.

### Book Details

- Amazon Sales Rank: #1313807 in Books
- Brand: Michael Green
- Published on: 2012-09-19
- Released on: 2012-08-22
- Original language: English
- Number of items: 1
- Dimensions: 9.20" h x 1.20" w x 6.10" l, 1.55 pounds
- Binding: Paperback
- 558 pages

### Features

- Linear Robust Control

## Editorial Reviews

From the Publisher

Intended for students and control engineers, this text provides an in-depth examination of the latest developments in modern optimal and robust control.

About the Author

## Customer Reviews

Most helpful customer reviews

1 of 1 people found the following review helpful.

Very Thorough and Rigorous Work in Robust Control Systems Theory

By Raymond Woo

Rigorous and mathematically intensive book written for those willing to learn - but be warned, it is not for the faint of heart and one should have the prerequisites prior to learning from this book. Readers who obtained a Master's degree in Electrical Engineering-Control Theory or in Applied Mathematics with some exposure to Control System concepts via the State Space approach are in a good position to learn from the book; a strong background in systems of linear differential equations, Linear Algebra and related Matrix Theory, and Mathematical Analysis (Real and Complex) should also come in handy. Typically assumed prerequisites are understanding of Linear Systems Theory via State Space (vector) representation, Probability and Stochastic Processes, and Optimal Control with some Optimization Theory essentials.

The concepts are clearly described and schematically illustrated with the aid of diagrams (control system block diagrams, with signal flows and feedback clearly depicted). The approach is somewhat geared to theorems and proofs in a typical mathematical format, though the underlying Control Theoretic concepts are well stated in a lucid fashion rather than tacitly or implicitly assumed. Of course, the ideas are step-wise laid out as the books progresses rapidly from rudiments and basics to moderately advanced and then to very advanced ideas and concepts underlying robustness without verbosity that is sometimes seen in similar books.

For instance, the approach taken in the first chapter is the introduction of the concept of robustness based on the very idea of insensitivity to system disturbances in general. A simple example introduced is a linear time-invariant system with a open-loop gain and a time-invariant controller one in tandem, together with full output feedback and zero input. The authors try to derive a simple equation with a unknown but for the time being time-invariant multiplicative feed forward parameter appearing in the equivalent small gain problem derived. A very simple criterion is derived assuming positive feedback instead of negative feedback. Then, in an implicit argument, the classical Nyquist stability criterion is applied with the +1 point (as opposed to -1) used as a reference. The result is a numerical bound imposed on the norm of the equivalent system gain taken by assumption over all possible system frequencies. From here, the authors apply the infinity-norm to the equivalent system gain, and proceed to examine the merits of finding a stabilizing controller that minimizes the system gain via the infinity-norm to accommodate the criterion of "applicable over all frequencies". The very rudimentary optimization problem with zero input illustrates the control system robustness problem in terms of optimal disturbance attenuation, leading to the introduction of the H-infinity optimal controller synthesis problem next, followed by optimal disturbance attenuation. The underlying ideas and thought process involved in the concept of robust in optimal control is step-wise laid out employing very simple feedback models, a powerful approach that captures the reader's attention and focus by capitalizing on the key concepts without the clutter of complicated mathematics, at least for starting off. Simple examples involving single input-single output are given along the way to illustrate the fundamental concepts being explained. But the authors are not delineating every single detail from a scratch - a fundamental background is implicitly assumed and inherently required. More often than not, as in many British scientific books, many of the details required for deriving a given equation are not explicitly stated and delineated but assumed to be implicitly understood - perhaps a caveat for the uninitiated and those without the proper prerequisites.

Down the road, linear optimal control problems appearing in multivariable systems are addressed. A strong foundation in the Linear Optimal Control Theory is required at this later stage.

All in all - a very good book, but may not be for the average knowledgeable reader in some self study fashion, being that it is a bit terse and highly nontrivial for some and very rigorous and intensive overall, requiring that one be fully equipped with the fundamentals called for in Modern Control Theory.

6 of 6 people found the following review helpful.

Very Good

By Me

I had the fortune to attend the course in Linear Robust Control with Dr. Green at Cornell University and used the book as a text. This book is perfect if you have a good understanding of linear algebra as well as optimal control theory. Some of the proposed problems are (I remember the headaches) of high dificulty but having the book along with some good papers written by the autors, makes them much easier. Because of the dificulty of the subject, I read several other books and none was better that this so if you really want to learn Linear Robust Control and care about mathematic rigurousity, this is the book for you. It is best suited as a companion for a course in robust control since the book is not easy at all.