Titlebook: Methods of Algebraic Geometry in Control Theory: Part II; Multivariable Linear Peter Falb Book 1999 Springer Science+Business Media New Yor

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攤位

The Laurent Isomorphism Theorem: II,Now we wish to give an appropriate algebraic structure to Hank(., ., .). One approach would be to consider the image of .(., ., .) under the Laurent map, which by Theorem 10.16, would be a quasi-projective variety and then to show the image is bijective to Hank(., ., .). We shall use a different approach here.

acclimate

Projective Algebraic Geometry IV: Families, Projections, Degree,We shall use the Main Theorem of Elimination Theory (10.16) to develop some families of varieties.

六邊形

The State Space: Realizations, Controllability, Observability, Equivalence,We have already introduced “realizations” in dealing with the transfer and Hankel matrices (see Chapter 3). In this chapter, we extend the theory developed in Part I (e.g., Chapters 10 and 11).

deficiency

Projective Algebraic Geometry V: Fibers of Morphisms,Our goal here is to extend and amplify the results of Part I, Chapter 18 for the projective situation. The term “variety” means either a projective or quasi-projective variety.

CARK

Projective Algebraic Geometry VI: Tangents, Differentials, Simple Subvarieties,We recall (I.20) that if .. is an affine variety and . ∈ .., then the (Zariski) ...., ..., is given by any of the following:

HERE

彎曲道理

Projective Algebraic Geometry VIII: Intersections,We shall examine in a brief elementary way the notion of intersection of varieties ([F-5], [H-3]). We shall eventually prove Bezout’s Theorem which plays a role in pole placement.

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故意

Methods of Algebraic Geometry in Control Theory: Part II978-1-4612-1564-6Series ISSN 2324-9749 Series E-ISSN 2324-9757