Appendix B. Analysis in R and Rⁿ

Chapters in this book

1. Frontmatter i
2. Contents v
3. List of Figures xi
4. Preface xiii
5. Chapter One. Introduction 1
6. Chapter Two. Mathematical Background 12
7. Chapter Three. Linear Systems and Stability 49
8. Chapter Four. Controllability of Linear Time Invariant Systems 82
9. Chapter Five. Observability and Duality 109
10. Chapter Six. Stabilizability of LTI Systems 124
11. Chapter Seven. Detectability and Duality 138
12. Chapter Eight. Stability Theory 161
13. Chapter Nine. Cascade Systems 189
14. Chapter Ten. Center Manifold Theory 212
15. Chapter Eleven. Zero Dynamics 233
16. Chapter Twelve. Feedback Linearization of Single-Input Nonlinear Systems 268
17. Chapter Thirteen. An Introduction to Damping Control 289
18. Chapter Fourteen. Passivity 302
19. Chapter Fifteen. Partially Linear Cascade Systems 331
20. Chapter Sixteen. Input-to-State Stability 359
21. Chapter Seventeen. Some Further Reading 378
22. Appendix A. Notation: A Brief Key 381
23. Appendix B. Analysis in R and Rⁿ 383
24. Appendix C. Ordinary Differential Equations 393
25. Appendix D. Manifolds and the Preimage Theorem; Distributions and the Frobenius Theorem 403
26. Appendix E. Comparison Functions and a Comparison Lemma 420
27. Appendix F. Hints and Solutions for Selected Exercises 430
28. Bibliography 443
29. Index 451