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

Sinopsis

1 Scalar Input or Scalar Output Systems.- 2 Two or Three Input, Two Output Systems: Some Examples.- 3 The Transfer and Hankel Matrices.- 4 Polynomial Matrices.- 5 Projective Space.- 6 Projective Algebraic Geometry I: Basic Concepts.- 7 Projective Algebraic Geometry II: Regular Functions, Local Rings, Morphisms.- 8 Exterior Algebra and Grassmannians.- 9 The Laurent Isomorphism Theorem: I.- 10 Projective Algebraic Geometry III: Products, Graphs, Projections.- 11 The Laurent Isomorphism Theorem: II.- 12 Projective Algebraic Geometry IV: Families, Projections, Degree.- 13 The State Space: Realizations, Controllability, Observability, Equivalence.- 14 Projective Algebraic Geometry V: Fibers of Morphisms.- 15 Projective Algebraic Geometry VI: Tangents, Differentials, Simple Subvarieties.- 16 The Geometric Quotient Theorem.- 17 Projective Algebraic Geometry VII: Divisors.- 18 Projective Algebraic Geometry VIII: Intersections.- 19 State Feedback.- 20 Output Feedback.- Appendices.- A Formal Power Series, Completions, Regular Local Rings, and Hubert Polynomials.- B Specialization, Generic Points and Spectra.- C Differentials.- D The Space.- E Review of Affine Algebraic Geometry.- References.- Glossary of Notations.

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