5R15. Dynamics of Controlled Mechanical Systems with Delayed Feedback. - H Hu and Z Wang (Inst of Vib Eng Res, Nanjing Univ of Aeronaut and Astronaut, Nanjing, 210016, PR China). Springer-Verlag, Berlin. 2002. 294 pp. ISBN 3-540-43733-9. \$89.95.

Reviewed by DB Schaechter (Lockheed Martin, Bldg 201, Org L9-24, 3251 Hanover St, Palo Alto CA 94304-1191).

Hu and Wang have compiled an engineering monograph that can be used as a reference for the subject title. Their text is suited for upper division control engineers, graduate students, and control engineering professionals, and presupposes knowledge of control systems, differential and difference equations, analysis, frequency response methods, and linear and nonlinear stability criteria. The text is divided into eight chapters dealing with modeling, fundamentals, stability analyses, periodic motions, chaotic systems, and control of delayed dynamic systems. It consists of good quality figures, a decent index, no problem sets, no appendices, several pages of references, and interesting highly analytical (theorem-proof) technical material solidified occasionally with seemingly contrived examples. Readability suffers slightly in places from lack of grammatical editing.

In the text, the authors present a formalized treatment of systems (both linear and nonlinear) containing delays (both single and multiple) and address both the stability and performance aspects of such systems. They present a refreshingly systematic and analytical approach to the subject matter, much more than just the $e−sT$ unity gain, linear phase impact of a constant time delay and its manifestations in linear systems. These techniques include, linear stability theory, Lyapunov stability, approximation techniques for short time delays, stability regions, delay independent stability, generalized Sturm stability, perturbation methods, and periodic behavior. A noticeable omission, perhaps by choice, is treatment at any length of Laplace transforms and how they might be applied to analyzing and designing controllers for such systems.

There is a wealth of relevant and detailed information pertaining to systems which encompass time delays, however, the sequence of chapters seems to be somewhat non-intuitive, at times, with occasional meandering away from the chapter topic. For example, Chapter 1, which deals with the modeling of delay dynamic systems, rapidly delves in unwarranted detail into genetic algorithm approaches for characterizing and identifying such systems. This chapter, in turn, is followed by an excellent chapter entitled Fundamentals of Delay Differential Equations, with content that one might expect pedagogically to serve as introductory material for the entire text. The remainder of the text then penetrates the core material of the book, how one characterizes, recognizes, analyzes, approximates, and controls systems in which single or multiple finite time delays play a significant role in the overall system response.

All in all, Dynamics of Controlled Mechanical Systems with Delayed Feedback would add depth and breadth to any engineering library and would prove beneficial to control engineers who would like to probe more deeply into some of the more subtle ramifications of the presence of time delays in mechanical systems.