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  • Algebraic and Differential Topology of Robust Stability

    Algebraic and Differential Topology of Robust Stability by Jonckheere, Edmond A.;

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      • Publisher's listprice GBP 102.50
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    48 969 Ft

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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
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    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.

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    Long 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.

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    Table 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

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