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Methods of algebraic geometry in control theory. Part II, Multivariable linear systems and projective algebraic geometry

Author: Peter L Falb
Publisher: New York : Springer Science+Business Media, LLC, [1999] ©1999
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry).

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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Peter L Falb
ISBN: 9781461215646 1461215641
OCLC Number: 889422556
Notes: Originally published: Boston : Birkhäuser, 1999.
Description: 1 online resource (viii, 390 pages)
Contents: 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 --
Index.
Other Titles: Multivariable linear systems and projective algebraic geometry
Responsibility: Peter Falb.

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"The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input-, two-output systems in detail. I highly recommend this Read more...

 
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