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Algebraic and differential topology of robust stability

Author: Edmond A Jonckheere
Publisher: New York : Oxford University Press, 1997.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Jonckheere, Edmond A., 1954-
Algebraic and differential topology of robust stability.
New York : Oxford University Press, 1997
(DLC) 95049073
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Edmond A Jonckheere
ISBN: 1429401230 9781429401234 019535768X 9780195357684 9780195093018 0195093011 1280527714 9781280527715
OCLC Number: 560383147
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.
Responsibility: Edmond A. Jonckheere ; with 79 pictures, computer generated by Chih-Yung Cheng, Chung-Kuang Chu, and Murilo G. Coutinho.

Abstract:

In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology from an application-oriented point of  Read more...

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