Methods of Algebraic Geometry in Control Theory: Part II Multivariable Linear Systems and Projective Algebraic Geometry

✍ Scribed by Falb P

• Publisher: Birkhauser; Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 384
• Series: Modern Birkhäuser Classics
• Category: Library

✦ Table of Contents

Contents......Page 7
Preface......Page 9
Introduction......Page 11
1: Scalar Input or Scalar Output Systems......Page 17
Exercises......Page 43
2: Two or Three Input, Two Output Systems: Some Examples......Page 44
Exercises......Page 65
3: The Transfer and Hankel Matrices......Page 67
Exercises......Page 85
4: Polynomial Matrices......Page 86
Exercises......Page 109
5: Projective Space......Page 111
Exercises......Page 118
6: Projective Algebraic Geometry I: Basic Concepts......Page 119
Exercises......Page 134
7: Projective Algebraic Geometry II: Regular Functions, Local Rings, Morphisms......Page 135
Exercises......Page 146
8: Exterior Algebra and Grassmannians......Page 148
Exercises......Page 165
9: The Laurent Isomorphism Theorem: I......Page 166
Exercises......Page 176
10: Projective Algebraic Geometry III: Products, Graphs, Projections......Page 177
Exercises......Page 184
11: The Laurent Isomorphism Theorem: II......Page 185
Exercises......Page 194
12: Projective Algebraic Geometry IV: Families, Projections, Degree......Page 195
Exercises......Page 204
13: The State Space: Realizations, Controllability, Observability, Equivalence......Page 205
Exercises......Page 225
14: Projective Algebraic Geometry V: Fibers of Morphisms......Page 226
15: Projective Algebraic Geometry VI: Tangents, Differentials, Simple Subvarieties......Page 234
Exercises......Page 245
16: The Geometric Quotient Theorem......Page 246
Exercises......Page 260
17: Projective Algebraic Geometry VII: Divisors......Page 262
Exercises......Page 273
18: Projective Algebraic Geometry VIII: Intersections......Page 274
19: State Feedback......Page 285
20: Output Feedback......Page 314
Exercises......Page 327
Appendix A: Formal Power Series, Completions, Regular Local Rings, and Hilbert Polynomials......Page 329
Appendix B: Specialization, Generic Points and Spectra......Page 348
Appendix C: Differentials......Page 355
Appendix D: The Space Cm......Page 358
Appendix E: Review of Affine Algebraic Geometry......Page 363
References......Page 370
Glossary of Notations......Page 375
Index......Page 377

✦ Subjects

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