| Description |
1 online resource (625 pages) |
| Contents |
List of Figures; List of Symbols; 1 Prologue; I: SIMPLICIAL APPROXIMATION AND ALGORITHMS; 2 Robust Multivariable Nyquist Criterion; 2.1 Multivariable Nyquist Criterion; 2.2 Robust Multivariable Nyquist Criterion; 2.3 Uncertainty Space; 2.4 ""Punctured"" Uncertainty Spaces; 2.5 Compactification of Imaginary Axis; 2.6 Horowitz Supertemplate Approach; 2.7 Crossover; 2.8 Mapping into Other Spaces; 3 A Basic Topological Problem; 3.1 The Boundary Problem; 3.2 Topology for Boundary and Continuity; 3.3 Mathematical Formulation of Boundary Problem; 3.4 Example (Continuous Fraction Criterion) |
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3.5 Example (Kharitonov)3.6 Example (Real Structured Singular Value); 3.7 Example (Brouwer Domain Invariance); 3.8 Example (Covering Map); 3.9 Example (Holomorphic Mapping); 3.10 Example (Proper Mapping); 3.11 Example (Conformal Mapping); 3.12 Examples (Horowitz); 3.13 Example (Functions on Polydisks); 3.14 Several Complex Variables; 3.15 Example (Plurisubharmonic functions); 3.16 Example (Proper Holomorphic and Biholomorphic Maps); 3.17 Example (Whitney's Root System); 4 Simplicial Approximation; 4.1 Simplexes, Complexes, and Polyhedra; 4.2 Abstract Complexes; 4.3 Alexandroff Theorem |
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4.4 Simplicial Approximation-Point Set Topology4.5 Simplicial Map-Algebra; 4.6 Computational Issues; 4.7 Relative Simplicial Approximation; 4.8 Cell Complexes and Cellular Maps; 4.9 Historical Notes; 5 Cartesian Product of Many Uncertainties; 5.1 Prismatic Decomposition; 5.2 Boundary of Cartesian Product; 5.3 Simplicial Combinatorics of Cube; 5.4 Q-Triangulation; 5.5 Combinatorial Equivalence; 5.6 Flatness; 6 Computational Geometry; 6.1 Delaunay Triangulation of Template; 6.2 Simplicial Edge Mapping; 6.3 The SimplicialVIEW Software; 6.4 Numerical Stability, Flatness, and Conditioning |
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6.5 Making Map (Locally) Simplicial6.6 Procedure; 7 Piecewise-Linear Nyquist Map; 7.1 Piecewise-Linear Nyquist Map; 7.2 From Piecewise-Linear to Simplicial Map; 7.3 Strict Linear Complementarity; 8 Game of the Hex Algorithm; 8.1 2-D Hex Board; 8.2 n-D Hex Board; 8.3 Combinatorial Equivalence; 8.4 Two-Dimensional Hex Game Algorithm; 8.5 Three-Dimensional Hex Game Algorithm; 8.6 Higher-Dimensional Hex Games; 9 Simplicial Algorithms; 9.1 Simplicial Algorithms Over 2-D Uncertainty Space; 9.2 Simplicial Algorithms Over 3-D Uncertainty Space; 9.3 Relative Uncertainty Complex |
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9.4 Simplicial Labeling Map9.5 Algorithm-Integer Search; 9.6 Algorithm-Vector Labeling Search; II: HOMOLOGY OF ROBUST STABILITY; 10 Homology of Uncertainty and Other Spaces; 10.1 Simplicial Homology; 10.2 Semisimplicial Homology; 10.3 Homology of a Chain Complex; 10.4 Homotopy Invariance; 10.5 Homology of Product of Uncertainty; 10.6 Uncertainty Manifold-Mayer-Vietoris Sequence; 10.7 Relative Homology Sequence; 10.8 More Sophisticated Homology Computation; 11 Homology of Crossover; 11.1 Combinatorial Homology of Crossover; 11.2 Projecting the Crossover; 12 Cohomology |
| Summary |
1. ProloguePart I: Simplicial approximations of algorithms 2. Robust multivariable Nyquist criterion3. A basic topological problem4. Simplicial approximation5. Cartesian product of many uncertainties6. Computational geometry7. Piece-wise Nyquist map8. Game of Hex algorithm9. Simplicial algorithmsPart II: Homology of robust stability 10. Homology of uncertainty and other spaces11. Homology of crossover12. Cohomology13. Twisted Cartesian product of uncertainty14. Spectral sequence of Nyquist mapPart III: Homotopy of robust stability 15. Homotopy groups and sequences16. Obstruction to extending t |
| Notes |
12.1 Simplicial Cohomology |
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Print version record |
| Subject |
Control theory.
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Algebraic topology.
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Differential topology.
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Algebraic topology.
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Control theory.
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Differential topology.
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| Form |
Electronic book
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| ISBN |
9780195357684 |
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019535768X |
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