A complex variable approach to the analysis of linear multivariable feedback systems [Book reviews

Abstract

Reciew by Christopher I. Byrnes. This book represents a basic and fundamental contribution to multivariable linear system theory, especially to the development of graphical multivariable frequency domain methods for system design. The text itself consists of an introduction, five chapters leading to a generalized Nyquist stability criterion, a generalized inverse Nyquist stability criterion, a chapter on root loci, and a final chapter on stability of systems depending on a parameter and other topics for future research. There are also seven appendices which develop assorted topics needed throughout the text, e.g., the definition of an algebraic function, methods for sketching the Riemann surfaces which occur, an extended principle of the argument, and more specific topics. In summary, it is the reviewer's opinion that this text is an important research monograph covering and, indeed malung, sigdicant and far reaching strides in the expanding field of frequency domain analysis of multivariable systems. It contains several seminal observations and developments in the area of system design, especially in the application of algebraic function theory to what is consequently a theory of multivariable root loci. and for this reason alone is indispensable for the researcher or graduate student interested in linear multivariable systems.