Algebraic and differential topology of robust stability /

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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 th...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Jonckheere, Edmond A., 1954-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York : Oxford University Press, 1997.
Temas:
Control theory.
Algebraic topology.
Differential topology.
Théorie de la commande.
Topologie algébrique.
Topologie différentielle.
TECHNOLOGY & ENGINEERING > Automation.
TECHNOLOGY & ENGINEERING > Robotics.
Algebraic topology
Control theory
Differential topology
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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