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

• Κύριος συγγραφέας: Falb, Peter (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Modern Birkhäuser Classics,
• Θέματα: Algebraic geometry.; System theory.; Control engineering.; Algebraic Geometry.; Systems Theory, Control.; Control and Systems Theory.

"An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic...

Πίνακας περιεχομένων:

• 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. Group 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
• Appendix A: Tensor Products
• Appendix B: Actions of Reductive Groups
• Appendix C: Symmetric Functions and Symmetric Group Actions
• Appendix D: Derivations and Separability
• Problems
• References.