This volume is the result of our teaching in the last few years of a
first- year graduate course on multivariable feedback systems addressed
to control engineers. The prerequisites are modest: an undergraduate
course in control (for acquaintance with concepts, terms, and design
goals) and a senior-graduate course in linear systems. This volume
covers lumped linear time-invariant multi-input multi-output systems
with strong emphasis on control problems. The purpose is to provide a
rapid introduction to some of the main and simpler results of control
theory and to provide access to the current literature. Note that our
exposition pays particular attention to the time-domain behavior of the
systems under study. Note also that we cover neither optimization nor
stochastic systems since these topics are treated in separate courses.
As is obvious from its abundant literature, multivariable control is a
very rapidly developing field. Consequently, we have no expectation that
our exposition will become definitive; however, we hope that our efforts
will be found useful. To get an idea of the contents, we suggest reading
carefully the table of contents and the introduction of the chapters.
Roughly, Chapter 1 is an introduction to feedback issues in a
multivariable context (desensitization, large gain, singular values,
etc. ). Chapters 2 and 3 cover the mathematical tools for handling
transfer functions as polynomial-matrix fractions and for studying
systems described by polynomial matrices. Chapter 4 uses these tools to
cover the general theory of interconnected systems.