After providing appropriate background material, this text describes algorithms to solve some of the basic problems in the design of control systems. The emphasis is on the sensitivity of the problems and the numerical behavior of the computational methods. Chapters 1 and 2 give the background material on numerical linear algebra and control theory, respectively. Chapters 3 to 5 present algorithms for the numerical solution of the problems described in chapter 2, the matrix exponential problem, stability analysis, system balancing and reduction, pole assignment, and system stabilization. Chapter 6 covers the numerical solution of matrix Ricatti equations. Finally, chapter 7 describes the numerical computation of geometric objects such as subspaces and angles. The text does not mention Laplace transform methods.
Chapters 1 and 2 are extreme condensations of material from standard texts, presenting only definitions and results without proofs. The section on round-off error and numerical stability contains more discussion and examples than other parts of chapter 1, but for the most part the first two chapters seem to be included only for review or as a guide for independent study.
The remainder of the book contains material gathered, to quote the preface, from “a great number of journal articles, symposium papers and technical reports.” The definitions and results are supported by more examples and explanation. For each problem, perturbation results are followed by the description of one or more algorithms with an assessment of their stability and the amount of work involved.
This book will be useful to engineers and graduate students who design or study control systems. Algorithm descriptions and computed examples make references to sources of written and tested software such as EISPAC and ACM Transactions on Mathematical Software. Many books on computational methods assume that effective programs follow immediately from algorithmic descriptions. In general, the writing style is dense. Although the authors expect the reader to go to outside material for details and clarification, the references are plentiful and clearly indicated.
