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E-book
Author Jonckheere, Edmond A., 1954-

Title Algebraic and differential topology of robust stability / Edmond A. Jonckheere ; with 79 pictures, computer generated by Chih-Yung Cheng, Chung-Kuang Chu, and Murilo G. Coutinho
Published New York : Oxford University Press, 1997
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Description 1 online resource (xlvi, 576 pages) : illustrations
Contents Cover -- Contents -- List of Figures -- List of Symbols -- 1 Prologue -- I58; SIMPLICIAL APPROXIMATION AND ALGORITHMS -- 2 Robust Multivariable Nyquist Criterion -- 1 Multivariable Nyquist Criterion -- 2 Robust Multivariable Nyquist Criterion -- 3 Uncertainty Space -- 4 34;Punctured34; Uncertainty Spaces -- 5 Compactification of Imaginary Axis -- 6 Horowitz Supertemplate Approach -- 7 Crossover -- 8 Mapping into Other Spaces -- 3 A Basic Topological Problem -- 346;1 The Boundary Problem -- 346;2 Topology for Boundary and Continuity -- 346;3 Mathematical Formulation of Boundary Problem -- 346;4 Example 40;Continuous Fraction Criterion41; -- 346;5 Example 40;Kharitonov41; -- 346;6 Example 40;Real Structured Singular Value41; -- 346;7 Example 40;Brouwer Domain Invariance41; -- 346;8 Example 40;Covering Map41; -- 346;9 Example 40;Holomorphic Mapping41; -- 346;10 Example 40;Proper Mapping41; -- 346;11 Example 40;Conformal Mapping41; -- 346;12 Examples 40;Horowitz41; -- 346;13 Example 40;Functions on Polydisks41; -- 346;14 Several Complex Variables -- 346;15 Example 40;Plurisubharmonic functions41; -- 346;16 Example 40;Proper Holomorphic and Biholomorphic Maps41; -- 346;17 Example 40;Whitney39;s Root System41; -- 4 Simplicial Approximation -- 446;1 Simplexes44; Complexes44; and Polyhedra -- 446;2 Abstract Complexes -- 446;3 Alexandroff Theorem -- 446;4 Simplicial Approximation8212;Point Set Topology -- 446;5 Simplicial Map8212;Algebra -- 446;6 Computational Issues -- 446;7 Relative Simplicial Approximation -- 446;8 Cell Complexes and Cellular Maps -- 446;9 Historical Notes -- 5 Cartesian Product of Many Uncertainties -- 546;1 Prismatic Decomposition -- 546;2 Boundary of Cartesian Product -- 546;3 Simplicial Combinatorics of Cube -- 546;4 Q45;Triangulation -- 546;5 Combinatorial Equivalence -- 546;6 Flatness -- 6 Computational Geometry -- 646;1 Delaunay Triangulation of Template -- 646;2 Simplicial Edge Mapping -- 646;3 The SimplicialVIEW Software -- 646;4 Numerical Stability44; Flatness44; and Conditioning -- 646;5 Making Map 40;Locally41; Simplicial -- 646;6 Procedure -- 7 Piecewise45;Linear Nyquist Map -- 746;1 Piecewise45;Linear Nyquist Map -- 746;2 From Piecewise45;Linear to Simplicial Map -- 746;3 Strict Linear Complementarity -- 8 Game of the Hex Algorithm -- 846;1 245;D Hex Board -- 846;2 n45;D Hex Board -- 846;3 Combinatorial Equivalence -- 846;4 Two45;Dimensional Hex Game Algorithm -- 846;5 Three45;Dimensional Hex Game Algorithm -- 846;6 Higher45;Dimensional Hex Games -- 9 Simplicial Algorithms -- 946;1 Simplicial Algorithms Over 245;D Uncertainty Space -- 946;2 Simplicial Algorithms Over 345;D Uncertainty Space -- 946;3 Relative Uncertainty Complex -- 946;4 Simplicial Labeling Map -- 946;5 Algorithm8212;Integer Search -- 946;6 Algorithm8212;Vector Labeling Search -- II58; HOMOLOGY OF ROBUST STABILITY -- 10 Homology of Uncertainty and O
Summary In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential topology from an application-oriented point of view. It is suitable for graduate students in engineering and/or applied mathematics, and academic researchers
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Algebraic topology.
Control theory.
Differential topology.
Form Electronic book
LC no. 95049073
ISBN 0195093011
019535768X
1280527714
1429401230 (electronic bk.)
9780195093018
9780195357684
9781280527715
9781429401234 (electronic bk.)
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