Methods of Algebraic Geometry in Control Theory

by Falb, Peter L.

• ISBN13: 9780817641139
• ISBN10: 0817641130
• Format: Hardcover
• Copyright: 1999-07-01
• Publisher: Birkhauser

Summary

Presents an introduction to the ideas of algebraic geometry in the motivated context of system theory, providing the basic ideas of algebraic geometry accessible to engineers and applied scientists. DLC: Control theory.

Table of Contents

Preface	vii
Introduction	1	(6)
1 Scalar Input or Scalar Output Systems	7	(28)
2 Two or Three Input, Two Output Systems: Some Examples	35	(24)
3 The Transfer and Hankel Matrices	59	(20)
4 Polynomial Matrices	79	(26)
5 Projective Space	105	(8)
6 Projective Algebraic Geometry I: Basic Concepts	113	(16)
7 Projective Algebraic Geometry II: Regular Functions, Local Rings, Morphisms	129	(14)
8 Exterior Algebra and Grassmannians	143	(18)
9 The Laurent Isomorphism Theorem: I	161	(12)
10 Projective Algebraic Geometry III: Products, Graphs, Projections	173	(8)
11 The Laurent Isomorphism Theorem: II	181	(10)
12 Projective Algebraic Geometry IV: Families, Projections, Degree	191	(10)
13 The State Space: Realizations, Controllability, Observability, Equivalence	201	(22)
14 Projective Algebraic Geometry V: Fibers of Morphisms	223	(8)
15 Projective Algebraic Geometry VI: Tangents, Differentials, Simple Subvarieties	231	(12)
16 The Geometric Quotient Theorem	243	(16)
17 Projective Algebraic Geometry VII: Divisors	259	(12)
18 Projective Algebraic Geometry VIII: Intersections	271	(12)
19 State Feedback	283	(30)
20 Output Feedback	313	(16)
APPENDICES	329	(46)
A Formal Power Series, Completions, Regular Local Rings, and Hilbert Polynomials	329	(20)
B Specialization, Generic Points and Spectra	349	(8)
C Differentials	357	(4)
D The Space C^(n)(m)	361	(6)
E Review of Affine Algebraic Geometry	367	(8)
References	375	(6)
Glossary of Notations	381	(2)
Index	383