The Resource Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry, by Peter Falb, (electronic resource)
Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry, by Peter Falb, (electronic resource)
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The item Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry, by Peter Falb, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry, by Peter Falb, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 "An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing mathematical rigor, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than on abstraction. While familiarity with Part I is helpful, it is not essential, since a considerable amount of relevant material is included here. Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains a clear presentation, with an applied flavor , of the core ideas in the algebrageometric treatment of scalar linear system theory. Part II extends the theory to multivariable systems. After delineating limitations of the scalar theory through carefully chosen examples, the author introduces seven representations of a multivariable linear system and establishes the major results of the underlying theory. Of key importance is a clear, detailed analysis of the structure of the space of linear systems including the full set of equations defining the space. Key topics also covered are the Geometric Quotient Theorem and a highly geometric analysis of both state and output feedback. Prerequisites are the basics of linear algebra, some simple topological notions, the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises, which are an integral part of the exposition throughout, combined with an index and extensive bibliography of related literature make this a valuable classroom tool or good selfstudy resource. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input, twooutput systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." —Publicationes Mathematicae, Debrecen "This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I.... In the first volume the simpler singleinput–singleoutput timeinvariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory.... Each chapter contains illustrative examples throughout and terminates with some exercises for further study." —Mathematical Reviews.
 Language
 eng
 Extent
 1 online resource (X, 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
 Isbn
 9783319965741
 Label
 Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry
 Title
 Methods of Algebraic Geometry in Control Theory: Part II
 Title remainder
 Multivariable Linear Systems and Projective Algebraic Geometry
 Statement of responsibility
 by Peter Falb
 Language
 eng
 Summary
 "An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing mathematical rigor, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than on abstraction. While familiarity with Part I is helpful, it is not essential, since a considerable amount of relevant material is included here. Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains a clear presentation, with an applied flavor , of the core ideas in the algebrageometric treatment of scalar linear system theory. Part II extends the theory to multivariable systems. After delineating limitations of the scalar theory through carefully chosen examples, the author introduces seven representations of a multivariable linear system and establishes the major results of the underlying theory. Of key importance is a clear, detailed analysis of the structure of the space of linear systems including the full set of equations defining the space. Key topics also covered are the Geometric Quotient Theorem and a highly geometric analysis of both state and output feedback. Prerequisites are the basics of linear algebra, some simple topological notions, the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises, which are an integral part of the exposition throughout, combined with an index and extensive bibliography of related literature make this a valuable classroom tool or good selfstudy resource. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input, twooutput systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." —Publicationes Mathematicae, Debrecen "This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I.... In the first volume the simpler singleinput–singleoutput timeinvariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory.... Each chapter contains illustrative examples throughout and terminates with some exercises for further study." —Mathematical Reviews.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Falb, Peter
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Modern Birkhäuser Classics
 Springer eBooks
 Springer eBooks.
 http://library.link/vocab/subjectName
 Geometry, algebraic
 Label
 Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry, by Peter Falb, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 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
 Control code
 9783319965741
 Dimensions
 unknown
 Extent
 1 online resource (X, 390 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319965741
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 3 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1060589585
 Label
 Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry, by Peter Falb, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 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
 Control code
 9783319965741
 Dimensions
 unknown
 Extent
 1 online resource (X, 390 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319965741
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 3 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1060589585
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/MethodsofAlgebraicGeometryinControlTheory/uu0oI9hA6Bc/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/MethodsofAlgebraicGeometryinControlTheory/uu0oI9hA6Bc/">Methods of Algebraic Geometry in Control Theory: Part II : Multivariable Linear Systems and Projective Algebraic Geometry, by Peter Falb, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>