Methods of Algebraic Geometry in Control Theory: Part I: Scalar Linear Systems and Affine Algebraic Geometry

Front Matter ....Pages i-xiii
 Scalar Linear Systems over the Complex Numbers  (Peter Falb)....Pages 5-8
 Scalar Linear Systems over a Field k  (Peter Falb)....Pages 9-14
 Factoring Polynomials  (Peter Falb)....Pages 15-19
 Affine Algebraic Geometry: Algebraic Sets  (Peter Falb)....Pages 20-23
 Affine Algebraic Geometry: The Hilbert Theorems  (Peter Falb)....Pages 24-28
 Affine Algebraic Geometry: Irreducibility  (Peter Falb)....Pages 29-31
 Affine Algebraic Geometry: Regular Functions and Morphisms I  (Peter Falb)....Pages 32-38
 The Laurent Isomorphism Theorem  (Peter Falb)....Pages 39-44
 Affine Algebraic Geometry: Regular Functions and Morphisms II  (Peter Falb)....Pages 45-49
 The Stage Space: Realizations  (Peter Falb)....Pages 50-57
 The Stage Space: Controllability, observability, Equivalence  (Peter Falb)....Pages 58-64
 Affine Algebraic Geometry: Products, Graphs and Projections  (Peter Falb)....Pages 65-70
 Group Actions, Equivalence and Invariants  (Peter Falb)....Pages 71-75
 The Geometric Quotient Theorem: Introduction  (Peter Falb)....Pages 76-82
 The Geometric Quotient Theorem: Closed Orbits  (Peter Falb)....Pages 83-86
 Affine Algebraic Geometry: Dimension  (Peter Falb)....Pages 87-102
 The Geometric Quotient Theorem: Open on Invariant Sets  (Peter Falb)....Pages 103-104
 Affine Algebraic Geometry: Fibers of Morphisms  (Peter Falb)....Pages 105-112
 The Geometric Quotient Theorem: The Ring of Invariants  (Peter Falb)....Pages 113-127
 Affine Algebraic Geometry: Simple Points  (Peter Falb)....Pages 128-136
 Feedback and the Pole Placement Theorem  (Peter Falb)....Pages 137-144
 Affine Algebraic Geometry: Varieties  (Peter Falb)....Pages 145-150
 Interlude  (Peter Falb)....Pages 151-167
Back Matter ....Pages 168-202