Algebraic and differential topology of robust stability
Algebraic topology Control theory Differential topology TECHNOLOGY & ENGINEERING sähkökirjat
Oxford University Press
1997
EISBN 9780195093018
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.
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.
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.
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.
