"An introduction to the ideas of algebraic geometry in the motivated
context of system theory." This describes this two volume work which has
been specifically written to serve the needs of researchers and students
of systems, control, and applied mathematics. Without sacrificing
mathematical rigor, the author makes the basic ideas of algebraic
geometry accessible to engineers and applied scientists. The emphasis is
on constructive methods and clarity rather than on abstraction. While
familiarity with Part I is helpful, it is not essential, since a
considerable amount of relevant material is included here.
Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains
a clear presentation, with an applied flavor, of the core ideas in the
algebra-geometric treatment of scalar linear system theory. Part II
extends the theory to multivariable systems. After delineating
limitations of the scalar theory through carefully chosen examples, the
author introduces seven representations of a multivariable linear system
and establishes the major results of the underlying theory. Of key
importance is a clear, detailed analysis of the structure of the space
of linear systems including the full set of equations defining the
space. Key topics also covered are the Geometric Quotient Theorem and a
highly geometric analysis of both state and output feedback.
Prerequisites are the basics of linear algebra, some simple topological
notions, the elementary properties of groups, rings, and fields, and a
basic course in linear systems. Exercises, which are an integral part of
the exposition throughout, combined with an index and extensive
bibliography of related literature make this a valuable classroom tool
or good self-study resource. The present, softcover reprint is designed
to make this classic textbook available to a wider audience.
"The exposition is extremely clear. In order to motivate the general
theory, the author presents a number of examples of two or three input-,
two-output systems in detail. I highly recommend this excellent book to
all those interested in the interplay between control theory and
algebraic geometry." -Publicationes Mathematicae, Debrecen
"This book is the multivariable counterpart of Methods of Algebraic
Geometry in Control Theory, Part I.... In the first volume the simpler
single-input-single-output time-invariant linear systems were considered
and the corresponding simpler affine algebraic geometry was used as the
required prerequisite. Obviously, multivariable systems are more
difficult and consequently the algebraic results are deeper and less
transparent, but essential in the understanding of linear control
theory.... Each chapter contains illustrative examples throughout and
terminates with some exercises for further study." -Mathematical
Reviews
