Algebraic and Differential Topology of Robust Stability
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Product details:
- Publisher OUP USA
- Date of Publication 26 June 1997
- ISBN 9780195093018
- Binding Hardback
- No. of pages624 pages
- Size 241x159x33 mm
- Weight 1045 g
- Language English
- Illustrations numerous line figures 0
Categories
Short description:
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 view. It is suitable for graduate students in engineering and/or applied mathematics, academic researchers and governmental laboratories.
MoreLong description:
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.
MoreTable of Contents:
I. Simplicial Approximation and Algorithms
Prologue
Robust Multivariable Nyquist Criterion
A Basic Topological Problem
Simplicial Approximation
Cartesian Product of Uncertainties
Computational Geometry
Piecewise Linear Nyquist Map
Game of Hex Algorithm
Simplicial Algorithms
II. Homology of Robust Stability
Homology of Uncertainty and Other Spaces
Homology of Crossover
Cohomology
Twisted Cartesian Product of Uncertainties
Spectral Sequence of Nyquist Map
III. Homotopy of Robust Stability
Homotopy Groups and Sequences
Obstruction to Extending Nyquist Map
Homotopy Classification of Nyquist Maps
Brouwer Degree of Nyquist Map
Homotopy of Matrix Return Difference Map
K-Theory of Robust Stabilization
IV. Differential Topology of Robust Stability
Compact Differentiable Uncertainty Manifolds
Singularity Over Stratified Uncertainty Space
Structural Stability of Crossover
V. Algebraic Geometry of Crossover
Geometry of Crossover
Geopmetry of Stability Boundary
Epilogue
Appendices