Methods of algebraic geometry in control theory : part 1 : Scalar linear systems and affine algebraic geometry

Methods of algebraic geometry in control theory : part 1 Scalar linear systems and affine algebraic geometry

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Auteur principal : Falb Peter L. (Auteur)
Format : Livre
Langue : anglais
Titre complet : Methods of algebraic geometry in control theory. part 1, Scalar linear systems and affine algebraic geometry / Peter Falb
Publié : Basel : Birkhäuser , 1990
Description matérielle : 1 vol. (VII-202 p.)
Collection : Systems & control (Print) ; vol. 4
Sujets :
Géométrie algébrique
Commande, Théorie de la
Anneaux associatifs
Modules (algèbre)
Catégories (mathématiques)
Théorie des systèmes
  • 0. Introduction
  • 1. Scalar linear systems over the complex numbers
  • 2. Scalar linear systems over a field k
  • 3. Factoring polynomials
  • 4. Affine algebraic geometry : algebraic sets
  • 5. Affine algebraic geometry : the Hilbert theorems
  • 6. Affine algebraic geometry : irreducibility
  • 7. Affine algebraic geometry : regular functions and morphisms I
  • 8. The Laurent isomorphism theorem
  • 9. Affine algebraic geometry : regular functions and morphisms II
  • 10. The state space : realizations
  • 11. The state space : controllability, observability, equivalence
  • 12. Affine algebraic geometry : products, graphs and projections
  • 13. Groups actions, equivalence and invariants
  • 14. The geometric quotient theorem : introduction
  • 15. The geometric quotient theorem : closed orbits
  • 16. Affine algebraic geometry : dimension
  • 17. The geometric quotient theorem : open on invariant sets
  • 18. Affine algebraic geometry : fibers of morphisms
  • 19. The geometric quotient theorem : the ring of invariants
  • 20. Affine algebraic geometry : simple points
  • 21. Feedback and the pole placement theorem
  • 22. Affine algebraic geometry : varieties
  • 23. Interlude