Algebraic and Differential Topology of Robust Stability

• 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

"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 robustnessanalysis 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 newapproaches 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 robustnessanalysis 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 newapproaches to robust stability. It will inspire research in control based on modern mathematics."--Mathematical Reviews