WRITING an up-to-date textbook is a delicate project, especially in the fast evolving and comprehensive field of modern control theory. Initially, there are two diverging approaches to systems analysis and design: the time-domain approach and the frequency-domain approach. The time-domain approach originates from the mechanical control problems where differential equations of motion are readily available; it has led to the development of the optimal control theory (Pontryagin; Bellman) and the geometric methods in the state space (Kalman; Wonham). Time-domain methods are inherently muitivariable and equally apply for linear stationary as for nonlinear or timevarying problems. The frequency-domain approach is the more common in electrical and chemical engineering and covers the classical stability analysis using Bode and Nyquist plots. The introduction of Rosenbrock's polynomial system matrix opened new perspectives to the frequency domain approach, especially the study of structural properties and system equivalence. Recently, considerable research effort has been devoted to constructing multivariable versions of the root-locus technique and the Nyquist criterion.
Apart from this divergent approach the authors also had to solve the discrepancy between theoretical results obtained by mathematical and engineering practice, where often only a rough system model and few measurements are available. Moreover, the greater part of the available theory is elaborated for continuous-time systems, whereas the application of the results requires direct computer control, so that a discrete system comes about.
Patel and Munro deal with both time-and frequency-domain techniques with equal emphasis on theoretical as on design problems. Their work is meant to be a textbook for a graduate course in control systems, as well as a reference book for researchers. The selection of subjects and their elaboration should be judged accordingly.
Over a third of the book is an exposition of a solid theoretical basis. This contains an interesting historical review of the development of modern control theory: some elements of linear algebra and a description of the common multivariable system representations, including canonical forms. The following chapter treats the computation and classification of poles and zeros in multivariable systems. The theoretical section of the book is fairly complete and well documented. Most of the material can, however, be found in earlier textbooks. A chapter on multivariable system inverses constitutes the transition between the theoretical part of the book and the design techniques.
The most obvious way to stabilize a linear system is shifting its characteristic values to suitable positions in the complex plane. Patel and Munro discuss pole assignment by output and state feedback and they present algorithms for designing dyadic and full-rank feedback matrices. The dual problem of construct-