Methods of Algebraic Geometry in Control Theory: Multivariable Linear Systems and Projective Algebraic Geometry Pt. 2 - Hardcover
Synopsis
1 Scalar Input or Scalar Output Systems.- 2 Two or Three Input, Two Output Some Examples.- 3 The Transfer and Hankel Matrices.- 4 Polynomial Matrices.- 5 Projective Space.- 6 Projective Algebraic Geometry Basic Concepts.- 7 Projective Algebraic Geometry Regular Functions, Local Rings, Morphisms.- 8 Exterior Algebra and Grassmannians.- 9 The Laurent Isomorphism I.- 10 Projective Algebraic Geometry Products, Graphs, Projections.- 11 The Laurent Isomorphism II.- 12 Projective Algebraic Geometry Families, Projections, Degree.- 13 The State Realizations, Controllability, Observability, Equivalence.- 14 Projective Algebraic Geometry Fibers of Morphisms.- 15 Projective Algebraic Geometry Tangents, Differentials, Simple Subvarieties.- 16 The Geometric Quotient Theorem.- 17 Projective Algebraic Geometry Divisors.- 18 Projective Algebraic Geometry 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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Methods of Algebraic Geometry in Control Theory: Multivariable Linear Systems and Projective Algebraic Geometry Pt. 2
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