EAN: 9781461271949

SYSTEMS & CONTROL FOUNDATIONS & APPLICATIONS ...

Control theory represents an attempt to codify  in mathematical terms  the principles and
techniques used in the analysis and design of control systems. Algebraic geometry may  in an
elementary way  be viewed as the study of the structure and properties of the solutions of
systems of algebraic equations. The aim of this book is to provide access to the methods of
algebraic geometry for engineers and applied scientists through the motivated context of
control theory .* The development which culminated with this volume began over twenty-five
years ago with a series of lectures at the control group of the Lund Institute of Technology in
Sweden. I have sought throughout to strive for clarity  often using constructive methods and
giving several proofs of a particular result as well as many examples. The first volume dealt
with the simplest control systems (i.e.  single input  single output linear time-invariant
systems) and with the simplest algebraic geometry (i.e.  affine algebraic geometry). While this
is quite satisfactory and natural for scalar systems  the study of multi-input  multi-output
linear time­ invariant control systems requires projective algebraic geometry. Thus  this
second volume deals with multi-variable linear systems and pro­ jective algebraic geometry. The
results are deeper and less transparent  but are also quite essential to an understanding of
linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory
is included along with a brief summary of affine algebraic geometry (Appendix E).

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