The book has 12 chapters and two appendices. The first chapter provides a generalintroduction to feedback design and delineates the steps involved in such a process. Chapter 2 reviews classical frequency domain techniques for the analysis and synthesis of feedback loops for single-input single out-put (SISO) systems and discusses various design tradeoffs facing a control engineer. The H-infinity problem based on weighted sensitivity is also introduced in the chapter,along with some typical performance weights. Chapter 3 provides and introduction to multi-input multi-output (MIMO) systems, by concentrating on singular value decomposition (SVD), multivariable control, and multivariable right-half plane (RHP) zeros. Two examples included demonstrate how MIMO systems are more sensitive to input gain uncertainty than SISO systems, thus motivating the need for more careful analysis of the former for robustness -- which is carried out later in the book.

Chapter 4 covers some standard elements of linear system theory, such as state-space descriptions, state controlability and observability, poles and zeros, stability and stabilization, and system norms. This is a rather comprehensive treatment of the topic, which serves to make the book self-sufficient as fas as background material goes.

Chapters 5 and 6 deal with the important topic of performance limitations in controller design, for SISO and MIMO systems, respectively. For the former, eight controlability rules have been introduced as necessary conditions to achieve acceptable control performance, and these have been illustrated by a chemical process application (a pH neutralization process). For the latter, the authors first discuss the fundamental limitations caused by RHP zeros on the sensitivity and complementary sensitivity functions, and then carefully cover the issues of functional controlability, RHP zeros and poles, disturbances, input constraints, and uncertainty. A valid point stressed by the authors is that performance limitations are more severe for MIMO systems than SISO systems in the case of RHP zeros and poles, and disturbances. Chapters 7 and 8 discuss uncertainty modeling. The former is devoted to SISO systems, in which context representation of uncertainty by real and complex perturbations are covered, and robust stability (RS) and robust performance (RP) are analyzed. In the latter, RS and RP are discussed in the presence of multiple perturbations, with the main analysis tool being the structured singular value, known shortly as µ. Part of the chapter is devoted to showing how an optimal (µ-minimizing) robust controller can be obtained using a D-K iteration, which involves solving a sequence of scaled H-infinity problems.

Chapter 9 builds on the methodologies introduced in the previous chapters and describes several practical procedures for multivariable controller design, with emphasis placed on H-infinuty loop shaping. For design problems where this technique is not effective or is too complex to apply (such as unstable plants with multiple gain crossover frequencies), the authors propose and briefly describe a number of other techniques, such as LQG design followed by H-infinity loop shaping, or a standard H-infinity with a stacked cost function as in S/KS mixed-sensitvity optimization. Chapter 10 adresses the issue of the selections of the variables to be controled,measured, and manipulated, and the links to connect them. It presents some quantitative, such as decentralized control, that could be used in such control structure designs.

Model reduction is the topic of Chapter 11, which addresses the issues of reducing the order the controller model, and its impact on controller performance. Three methods, all of which are based on balanced residualization, have been presented in a comparative way: balanced truncation, balanced residualization, and the optimal Hankel norm approximation. One of the important observations made is that residualization preforms better at low and medium frequncies, while the other two methods perform better at high frequencies. Chapter 12 presents thress case studies which serve to illustrate several practical issues that are critical to multivariable controller design, such as weights selection in H-infinity loop-shaping design, ill-conditioned plants, µ analysis, and µ synthesis. The case studies discussed involve helicopter control, aero-engine control, and control of a distillation process. The first appendix provides the necessary background material on matrices and matrix norms,and the second discusses some spossible projects for students to carry out,and also presents a sample final exam.

As the authors indicate in the preface, this book could serve as a textbook i afirst-year graduate course on controller design in engineering departments. Being rich in insights and practical tips on controller design, the book should also prove to be very beneficial to industrial control engineers, both as a reference and as an educational tool. The authors have included several MATLAB files in the book to supplement the design tools presented, and have also made them (as well assolutions to selected exercisees) available over the internet -- which is a welcome new feature.

Overall,being competently written and easy to read, Multivariable Feedback Control: Analysis and Design is a valuable contribution to control literature and should appeal to practitioners of control as well as control theorists.