Algebraic and Differential Topology of Robust Stability

ISBN: 9780195093018 出版年：1997 页码：625 Jonckheere, Edmond A Oxford University Press

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