All chapters conclude with

*Exercises*.

**1. Introduction.**

Nonlinear Models and Nonlinear Phenomena. Examples.

**2. Second-Order Systems.**

Qualitative Behavior of Linear Systems. Multiple Equilibria. Qualitative Behavior Near Equilibrium Points. Limit Cycles. Numerical Construction of Phase Portraits. Existence of Periodic Orbits. Bifurcation. Systems.

**3. Fundamental Properties.**

Existence and Uniqueness. Continuos Dependence on Initial Conditions and Parameters. Differentiability of solutions and Sensitivity Equations. Comparison Principle.

**4. Lyapunov Stability.**

Autonomous Systems. The Invariance Principle. Linear Systems and Linearization. Comparison Functions. Nonautonomous Systems. Linear Time-Varying Systems and Linearization. Converse Theorems. Boundedness and Ultimate Boundedness. Input-to-State Stability.

**5. Input-Output Stability.**

*L* Stability. *L* Stability of State Models. *L*<v>2 Gain. Feedback Systems: The Small-Gain Theorem.

**6. Passivity.**

Memoryless Functions. State Models. Positive Real Transfer Functions. *L*<v>2 and Lyapunov Stability. Feedback Systems: Passivity Theorems.

**7. Frequency-Domain Analysis of Feedback Systems.**

Absolute Stability. The Describing Function Method.

**8. Advanced Stability Analysis.**

The Center Manifold Theorem. Region of Attraction. Invariance-like Theorems. Stability of Periodic Solutions.

**9. Stability of Perturbed Systems.**

Vanishing Pertubation. Nonvanishing Pertubation. Comparison Method. Continuity of Solutions on the Infinite Level. Interconnected Systems. Slowly Varying Systems.

**10. Perturbation Theory and Averaging.**

The Perturbation Method. Perturbation on the Infinite Level. Periodic Perturbation of Autonomous Systems. Averaging. Weekly Nonlinear Second-Order Oscillators. General Averaging.

**11. Singular Perturbations.**

The Standard Singular Perturbation Model. Time-Scale Properties of the Standard Model. Singular Perturbation on the Infinite Interval. Slow and Fast Manifolds. Stability Analysis.

**12. Feedback Control.**

Control Problems. Stabilization via Linearization. Integral Control. Integral Control via Linearization. Gain Scheduling.

**13. Feedback Linearization.**

Motivation. Input-Output Linearization. Full-State Linearization. State Feedback Control.

**14. Nonlinear Design Tools.**

Sliding Mode Control. Lyapunov Redesign. Backstepping. Passivity-Based Control. High-Gain Observers.

**Appendix A. Mathematical Review.** **Appendix B. Contraction Mapping.** **Appendix C. Proofs.** **Notes and References.** **Bibliography.** **Symbols.** **Index.**