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Invariance and system theory: algebraic and geometric aspects

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Bibliographic Details
Main Author:	Tannenbaum, Allen (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 1981
Series:	Lecture notes in mathematics 845
Subjects:	Invariants Modules, Théorie des Modules, théorie des Systèmes, Analyse de Systèmes, analyse de Moduli theory System analysis Invarianz Systemtheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000611088&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	IX, 161 S. graph. Darst.
ISBN:	3540105654 0387105654

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adam_text	TABLE OF CONTENTS Introduction Notation and Terminology Part I. Some Basic Algebraic Geometry 1 1. Affine Geometry 1 2. Projective Geometry 3 3. Regular Mappings 6 4. The Constructibility Theorem of Chevalley 9 5. Sheaves and Vector Bundles 10 6. The Grassman Variety 14 7. Some Remarks on Algebraic Geometry Over a Non Algebraically Closed Field 16 Part II. Some Basic System Theory 18 1. Dynamical Systems 18 2. Controllability and Reachability 22 3. Constructibility and Observability 24 4. State Variables 26 5. Transfer Functions 32 Part III. Invariant Theory and Orbit Space Problems 36 1. Algebraic Groups 36 2. On the Moduli of Endomorphisms 38 3. Quotients 42 4. Reductive Groups and Hilbert s 14th Problem 44 5. Richardson s Criterion 46 Part IV. Global Moduli of Linear Time Invariant Dynamical Systems 48 1. Complete Reachability and Pre Stability 48 2. Construction of the Quotient Space of Completely Reachable Pairs 53 3. Moduli of Linear Time Invariant Dynamical Systems 54 4. The Geometric Structure of the Moduli Space 57 5. The Global Moduli of Completely Reachable Matrix Triples 59 6. Some Open Problems 63 Part V. Local Moduli of Linear Time Invariant Dynamical Systems 65 1. Versal Deformations of Matrix Pairs 66 2. The Control Canonical Form 68 3. On the Construction of Holomorphic Canonical Forms 71 4. Versal Deformations of Matrix Triples 74 Part VI. Algebraic Realization Theory 76 1. Input/Output Maps and Abstract Realization Theory 76 2. Hankel Matrices 80 3. Realizations of Rational Matrices 84 4. Partial Realizations 87 5. Systems over Rings 89 6. Polynomial Systems 96 Part VII. On the Geometry of Rational Transfer Functions 104 1. Cauchy Indices and the Connected Components of Rat(n) 104 2. Complex Transfer Functions 108 3. The Topology of Rat(n) 113 4. Partial Realizations (Again) 116 VI Part VIII. Feedback and Stabilization of Systems with Parameter Uncertainty 119 1. Classical Stability Theory 119 2. Kronecker Indices and State Feedback 122 3. Coefficient and Pole Assignability 130 4. Blending and Output Feedback 133 5. Interpolation in the Unit Disc 139 6. Feedback Stabilization of Plants with Uncertainty in the Gain Factor 143 Bibliography 150 Index 158
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series	Lecture notes in mathematics
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spellingShingle	Tannenbaum, Allen Invariance and system theory algebraic and geometric aspects Lecture notes in mathematics Invariants Invariants ram Modules, Théorie des Modules, théorie des ram Systèmes, Analyse de Systèmes, analyse de ram Moduli theory System analysis Invarianz (DE-588)4120518-2 gnd Systemtheorie (DE-588)4058812-9 gnd
subject_GND	(DE-588)4120518-2 (DE-588)4058812-9
title	Invariance and system theory algebraic and geometric aspects
title_auth	Invariance and system theory algebraic and geometric aspects
title_exact_search	Invariance and system theory algebraic and geometric aspects
title_full	Invariance and system theory algebraic and geometric aspects Allen Tannenbaum
title_fullStr	Invariance and system theory algebraic and geometric aspects Allen Tannenbaum
title_full_unstemmed	Invariance and system theory algebraic and geometric aspects Allen Tannenbaum
title_short	Invariance and system theory
title_sort	invariance and system theory algebraic and geometric aspects
title_sub	algebraic and geometric aspects
topic	Invariants Invariants ram Modules, Théorie des Modules, théorie des ram Systèmes, Analyse de Systèmes, analyse de ram Moduli theory System analysis Invarianz (DE-588)4120518-2 gnd Systemtheorie (DE-588)4058812-9 gnd
topic_facet	Invariants Modules, Théorie des Modules, théorie des Systèmes, Analyse de Systèmes, analyse de Moduli theory System analysis Invarianz Systemtheorie
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work_keys_str_mv	AT tannenbaumallen invarianceandsystemtheoryalgebraicandgeometricaspects

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