| List of Figures | p. xi |
| Preface | p. xiii |
| Introduction | p. 1 |
| Open Loop Control | p. 1 |
| The Feedback Stabilization Problem | p. 2 |
| Chapter and Appendix Descriptions | p. 5 |
| Notes and References | p. 11 |
| Mathematical Background | p. 12 |
| Analysis Preliminaries | p. 12 |
| Linear Algebra and Matrix Algebra | p. 12 |
| Matrix Analysis | p. 17 |
| Ordinary Differential Equations | p. 30 |
| Phase Plane Examples: Linear and Nonlinear | p. 35 |
| Exercises | p. 44 |
| Notes and References | p. 48 |
| Linear Systems and Stability | p. 49 |
| The Matrix Exponential | p. 49 |
| The Primary Decomposition and Solutions of LTI Systems | p. 53 |
| Jordan Form and Matrix Exponentials | p. 57 |
| Jordan Form of Two-Dimensional Systems | p. 58 |
| Jordan Form of n-Dimensional Systems | p. 61 |
| The Cayley-Hamilton Theorem | p. 67 |
| Linear Time Varying Systems | p. 68 |
| The Stability Definitions | p. 71 |
| Motivations and Stability Definitions | p. 71 |
| Lyapunov Theory for Linear Systems | p. 73 |
| Exercises | p. 77 |
| Notes and References | p. 81 |
| Controllability of Linear Time Invariant Systems | p. 82 |
| Introduction | p. 82 |
| Linear Equivalence of Linear Systems | p. 84 |
| Controllability with Scalar Input | p. 88 |
| Eigenvalue Placement with Single Input | p. 92 |
| Controllability with Vector Input | p. 94 |
| Eigenvalue Placement with Vector Input | p. 96 |
| The PBH Controllability Test | p. 99 |
| Linear Time Varying Systems: An Example | p. 103 |
| Exercises | p. 105 |
| Notes and References | p. 108 |
| Observability and Duality | p. 109 |
| Observability, Duality, and a Normal Form | p. 109 |
| Lyapunov Equations and Hurwitz Matrices | p. 117 |
| The PBH Observability Test | p. 118 |
| Exercises | p. 121 |
| Notes and References | p. 123 |
| Stabilizability of LTI Systems | p. 124 |
| Stabilizing Feedbacks for Controllable Systems | p. 124 |
| Limitations on Eigenvalue Placement | p. 128 |
| The PBH Stabilizability Test | p. 133 |
| Exercises | p. 134 |
| Notes and References | p. 136 |
| Detectability and Duality | p. 138 |
| An Example of an Observer System | p. 138 |
| Detectability, the PBH Test, and Duality | p. 142 |
| Observer-Based Dynamic Stabilization | p. 145 |
| Linear Dynamic Controllers and Stabilizers | p. 147 |
| LQR and the Algebraic Riccati Equation | p. 152 |
| Exercises | p. 156 |
| Notes and References | p. 159 |
| Stability Theory | p. 161 |
| Lyapunov Theorems and Linearization | p. 161 |
| Lyapunov Theorems | p. 162 |
| Stabilization from the Jacobian Linearization | p. 171 |
| Brockett's Necessary Condition | p. 172 |
| Examples of Critical Problems | p. 173 |
| The Invariance Theorem | p. 176 |
| Basin of Attraction | p. 181 |
| Converse Lyapunov Theorems | p. 183 |
| Exercises | p. 183 |
| Notes and References | p. 187 |
| Cascade Systems | p. 189 |
| The Theorem on Total Stability | p. 189 |
| Lyapunov Stability in Cascade Systems | p. 192 |
| Asymptotic Stability in Cascades | p. 193 |
| Examples of Planar Systems | p. 193 |
| Boundedness of Driven Trajectories | p. 196 |
| Local Asymptotic Stability | p. 199 |
| Boundedness and Global Asymptotic Stability | p. 202 |
| Cascades by Aggregation | p. 204 |
| Appendix: The Poincarn++e-Bendixson Theorem | p. 207 |
| Exercises | p. 207 |
| Notes and References | p. 211 |
| Center Manifold Theory | p. 212 |
| Introduction | p. 212 |
| An Example | p. 212 |
| Invariant Manifolds | p. 213 |
| Special Coordinates for Critical Problems | p. 214 |
| The Main Theorems | p. 215 |
| Definition and Existence of Center Manifolds | p. 215 |
| The Reduced Dynamics | p. 218 |
| Approximation of a Center Manifold | p. 222 |
| Two Applications | p. 225 |
| Adding an Integrator for Stabilization | p. 226 |
| LAS in Special Cascades: Center Manifold Argument | p. 228 |
| Exercises | p. 229 |
| Notes and References | p. 231 |
| Zero Dynamics | p. 233 |
| The Relative Degree and Normal Form | p. 233 |
| The Zero Dyna | |
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