Multivariable linear systems and projective algebraic geometry
Peter Falb
This monograph is an introduction to the ideas of algebraic geometry written for graduate students in systems, control, and applied mathematics. An extension of an earlier volume, this self-contained work has an applied flavor in its presentation of the core ideas in the algebro-geometric treatment of scalar linear system theory with the emphasis on constructive methods rather than on abstraction. Exercises, which are an integral part of the exposition throughout, five appendices containing supplementary material, and extensive bibliography of related literature make this a valuable classroom tool or good self-study resource.
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[目次]
Scalar input or scalar output systems
two or three input, two output systems - some examples
the transfer and Hankel matrices
polynomial matrices
projective space
projective algebraic geometry I - basic concepts
projective algebraic geometry II - regular functions, local rings, morphisms
exterior algebra and grassmannians
the Laurent isomorphism theorem I
projective algebraic geometric III - products, projections, degree
the Laurent isomorphism theorem II
projective algebraic geometry IV - families, projections, degree
the state space - realizations, controllability, observability, equivalence
projective algebraic geometry V - fibres of morphisms
projective algebraic geometry VI - tangents, differentials, simple subvarieties
the geometry quotient theorem
projective algebraic geometry VII -divisors
projective algebraic geometry VIII - intersections
state feedback
output feedback
formal power series, completions, regular local rings, and Hilbert polynomials
specialization, generic points and spectra
differentials
the space nm
review of affine algebraic geometry.
「Nielsen BookData」より
[目次]
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.
「Nielsen BookData」より
書名
Multivariable linear systems and projective algebraic geometry