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.
Rezensionen / Stimmen
"The opening sentence of the monograph reads as follows: 'In this book, two seemingly unrelated fields of intellectual endeavor--algebraic/differential topology and robust control--are brought together.' Indeed, there are probably just a few control engineers who are familiar with the modern concepts of algebraic and differential topology; others need strong motivation to learn these disciplines. The book under review attempts to convince experts in robustness
analysis to do this and to provide the needed material to learn. . . . The book consists of 7 parts, which contain 26 chapters and 4 appendices. . . . [T]his book is a serious attempt to develop new
approaches to robust stability. It will inspire research in control based on modern mathematics."--Mathematical Reviews
"The opening sentence of the monograph reads as follows: 'In this book, two seemingly unrelated fields of intellectual endeavor--algebraic/differential topology and robust control--are brought together.' Indeed, there are probably just a few control engineers who are familiar with the modern concepts of algebraic and differential topology; others need strong motivation to learn these disciplines. The book under review attempts to convince experts in robustness
analysis to do this and to provide the needed material to learn. . . . The book consists of 7 parts, which contain 26 chapters and 4 appendices. . . . [T]his book is a serious attempt to develop new
approaches to robust stability. It will inspire research in control based on modern mathematics."--Mathematical Reviews
Sprache
Verlagsort
Zielgruppe
Illustrationen
Maße
Höhe: 243 mm
Breite: 163 mm
Dicke: 33 mm
Gewicht
ISBN-13
978-0-19-509301-8 (9780195093018)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Department of Electrical Engineering SystemsDepartment of Electrical Engineering Systems, University of Southern California, USA
I. SIMPLICIAL APPROXIMATION AND ALGORITHMS ; 1. Prologue ; 2. Robust Multivariable Nyquist Criterion ; 3. A Basic Topological Problem ; 4. Simplicial Approximation ; 5. Cartesian Product of Uncertainties ; 6. Computational Geometry ; 7. Piecewise Linear Nyquist Map ; 8. Game of Hex Algorithm ; 9. Simplicial Algorithms ; II. HOMOLOGY OF ROBUST STABILITY ; 10. Homology of Uncertainty and Other Spaces ; 11. Homology of Crossover ; 12. Cohomology ; 13. Twisted Cartesian Product of Uncertainties ; 14. Spectral Sequence of Nyquist Map ; III. HOMOTOPY OF ROBUST STABILITY ; 15. Homotopy Groups and Sequences ; 16. Obstruction to Extending Nyquist Map ; 17. Homotopy Classification of Nyquist Maps ; 18. Brouwer Degree of Nyquist Map ; 19. Homotopy of Matrix Return Difference Map ; 20. K-Theory of Robust Stabilization ; IV. DIFFERENTIAL TOPOLOGY OF ROBUST STABILITY ; 21. Compact Differentiable Uncertainty Manifolds ; 22. Singularity Over Stratified Uncertainty Space ; 23. Structural Stability of Crossover ; V. ALGEBRAIC GEOMETRY OF CROSSOVER ; 24. Geometry of Crossover ; 25. Geopmetry of Stability Boundary ; Epilogue ; Appendices
