Review of the book
S. Skogestad and I. Postlethwaite, Multivariable feedback control - Analysis and design, Wiley, 1996.
Reviewed by L. Bakule (Praha)
Zentralblatt für Mathematik, vol. 883,1998


The book, consisting of a preface, 12 chapters, 2 appendices, a bibliography and an index, deals with practical feedback control for linear systems emphasizing results that enhance insight and intuition. A brief outline of control process is given in the introduction (Ch. 1). Classical feedback control (Ch. 2), Introduction to multivariable control (Ch. 3) and Elements of linear system theory (Ch. 4) include standard topics with emphasis on classical frequency-domain methods and analysis of directions in multivariable systems using the singular value decomposition. Limitations of performance in SISO systems (Ch. 5) and in MIMO systems (Ch. 6) summarize fundamental limitations on performance using the concept of input-output controllability analysis (inherent control limitations in the plant). Uncertainty and robustness for SISO systems (Ch. 7) and Robustness stability and performance analysis (Ch. 8) cover uncertainty representation by real and complex real and complex perturbations. The structured singular value µ is the main analysis tool. The "optimal" robust controller design in terms of minimizing µ is described using DK-iteration. Controller design (Ch. 9) presents practical procedures for multivariable controller design. Control structure design (Ch. 10) summarizes some basic concepts for large-scale system control structure selection and decentralized control. Model reduction (Ch. 11) describes methods for reducing the order of a plant or of a controller model. Case studies (Ch. 12) includes three case studies illustrating a number of important practical issues. Matrix theory and norms (A.A) is included as background material for the book. In Project work and sample exam (A.B), a project outline is given together with a simple exam. Numerous worked-out examples make frequent use of MATLAB. Most of these use the µ toolbox. MATLAB source files, files used to generate figures and tables, models for plants, corrections, errors, etc. ... are available on the authors' home pages under the internet addresses given in the book. The book provides a very readble text appropraite both as an introductory graduate course and as an advanced undergraduate course in multivariable control. It will be certainly highly appreciated by specialists dealing with practical feedback control. It will serve as an excellent source of information for engineers who want to understand multivariable control with its limitations, and how it can be applied in practice.