ContentsPrefaceChapter 1: Introduction1.1 Nonlinear Models and Nonlinear Phenomena1.2 Examples1.2.1 Pendulum Equation1.2.2 Tunnel-Diode Circuit1.2.3 Mass-Spring System1.2.4 Negative-Resistance Oscillator1.2.5 Artificial Neural Network 1.2.6 Adaptive Control1.2.7 Common Nonlinearities

1.3 Exercises

Chapter 2: Second-Order Systems2.1 Qualitative Behaviour of Linear Systems2.2 Multiple EquilibriaQualitative Behaviour Near Equilibrium Points2.4 Limit Cycles2.5 Numerical Construction of Phase Portrait 2.6 Existence of Periodic Orbit 2.7 Bifurcation 2.8 Exercises

Chapter 3: Fundamental Properties3.1 Existence and Uniqueness3.2 Continuous Dependence on Initial Conditions and Parameters3.3 Differentiability of Solutions and Sensitivity Equations 3.4 Comparison Principle3.5 Exercises

Chapter 4: Lyapunov Stability 4.1 Autonomous Systems4.2 The invariance Principle4.3 Linear Systems and Linearization4.4 Comparison Functions4.5 Nonautonomous Systems4.6 Linear Time-Varying Systems and Linearization4.7 Converse Theorems4.8 Boundedness and Ultimate Boundedness 4.9 Input-to-State Stability 4.10 Exercises

Chapter 5: Input-Output Stability5.1 L Stability5.2 L Stability of State Models5.3 L2 Gain5.4 Feedback Systems: The Small-Gain Theorem5.5 Exercises

Chapter 6: Passivity6.1 Memoryless Functions6.2 State Models6.3Positive Real Transfer Functions 6.4 L2 and Lyapunov Stability6.5 Feedback Systems: Passivity Theorems6.6 Exercises

Chapter 7: Frequncy Domain Analysis of Feedback Systems7.1 Absolute Stability7.1.1 Circle Criterion7.1.2 Popov Criterion

7.2 The Describing Function Method7.3 Exercises

Chapter 8: Advanced Stability Analysis8.1 The Center Manifold Theorem8.2 Region of Attraction8.3 Invariance-like TheoremsStability of Periodic Solutions

Chapter 9: Stability of Perturbed Systems9.1 Vanishing Perturbation9.2 Nonvanishing Perturbation9.3 Comparison Method9.4 Continuity of Solutions on the Infinite Interval9.5Interconnected Systems 9.6 Slowly Varying Systems9.7 Exercises

Chapter 10: Perurbation Theory and Averaging10.1 The Perturbation Method10.2 Perturbation on the Infinite Interval10.3 Periodic Perturbation of Autonomous Systems10.4 Averagin10.5 Weakly Nonlinear Second-Order Oscillators10.6 General Averaging10.7 Exercises

Chapter 11: Singular Perturbation11.1 The Standard Singular Perturbation Model11.2 Time-Scale Properties of the Standard Model11.3 Singular Perturbation on the Infinite Interval11.4 Slow and Fast Manifolds11.5 Stability Analysis11.6 Exercises

Chapter 12: Feedback Control12.1 Control Problems12.2 Stabilization via Linearization12.3 Integral Control12.4 Integral Control via Linearization12.5 Gain Scheduling12.6 Exercises

Chapter 13: Feedback LinearizationChapter 14: Nonlinear Design Tools14.1 Sliding Mode Control14.1.1 Motivating Example14.1.2 Stabilization14.1.3 Tracking14.1.4 Regulation via Integral Control

14.2 Lyapunov Redesign14.2.1 Stabilization14.2.2 Nonlinear Damping

14.3 Backstepping14.4 Passivity-Based Control14.5 High-Gain Observers14.5.1 Motivating Example14.5.2 Stabilization14.5.3 Regulation via Integral Control

14.6 Exercises

Appendix A: Mathematical ReviewAppendix B: Contraction MappingAppendix C: ProofsC.1 Proof of Theorems 3.1 and 3.2C.2 Proof of Lemma 3.4C.3 Proof of Lemma 4.1C.4 Proof of Lemma 4.3C.5 Proof of Lemma 4.4C.6 Proof of LemmaC.7 Proof of Theorem 4.16C.8 Proof of Theorem 4.17C.9 Proof of Theorem 4.18C.10 Proof of Theorem 5.4C.11 Proofof Lemma 6.1C.12 Proof of Lemma 6.2C.13 Proof of Lemma 7.1C.14 Proof of Theorem 7.4C.15 Proof of Theorems 8.1 and 8.3C.16 Proof of Lemma 8.1C.17 Proof of Theorem 11.1C.18 Proof of Theorem 11.2C.19 Proof of Theorem 12.1C.20 Proof of Theorem 12.2C.21 Proof of Theorem 13.1C.22 Proof of Theorem 13.2C.23 Proof of Theorem 14.6

Notes and ReferencesBibliographySymbolsIndex