Contents 1 Introduction 1.1 Nonlinear Models and Nonlinear Phenomena 1.2 Examples 1.2.1 Pendulum Equation 1.2.2 Tunnel-Diode Circuit 1.2.3 Mass-Spring System 1.2.4 Negative-Resistance Oscillator 1.2.5 Artificial Neural Network 1.2.6 Adaptive Control 1.2.7 Common Nonlinearities 1.3 Exercises 2 Second-Order Systems 2.1 Qualitative Behavior of Linear Systems 2.2 Multiple Equilibria 2.3 Qualitative Behavior Near Equilibrium Points 2.4 Limit Cycles 2.5 Numerical Construction of Phase Portraits 2.6 Existence of Periodic Orbits 2.7 Bifurcation 2.8 Exercises 3 Fundamental Properties 3.1 Existence and Uniqueness 3.2 Continuous Dependence on Initial Conditions and Parameters 3.3 Differentiability of Solutions and Sensitivity Equations 3.4 Comparison Principle 3.5 Exercises 4 Lyapunov Stability 4.1 Autonomous Systems 4.2 The Invariance Principle 4.3 Linear Systems and Linearization 4.4 Comparison Functions 4.5 Nonautonomous Systems 4.6 Linear Time-Varying Systems and Linearization 4.7 Converse Theorems 4.8 Boundedness and Ultimate Boundedness 4 9 Input-to-State Stability 4.10 Exercises 5 Input-Output Stability 5.1 L Stability 5.2 L1 Stability of State Models 5.3 L2 Gain 5.4 Feedback Systems: The Small-Gain Theorem 5.5 Exercises 6 Passivity 6.1 Memoryless Functions 6.2 State Models 6.3 Positive Real Transfer Functions 6.4 L2 and Lyapunov Stability 6.5 Feedback Systems: Passivity Theorems 6.6 Exercises 7 Frequency Domain Analysis of Feedback Systems 7.1 Absolute Stability 7.1.1 Circle Criterion 7.1.2 Popov Criterion 7.2 The Describing Function Method 7.3 Exercises 8 Advanced Stability Analysis 8.1 The Center Manifold Theorem 8.2 Region of Attraction 8.3 Invariance-like Theorems 8.4 Stability of Periodic Solutions 8.5 Exercises 9 Stability of Perturbed Systems 9.1 Vanishing Perturbation 9.2 Nonvanishing Perturbation 9.3 Comparison Method 9.4 Continuity of Solutions on the Infinite Interval 9.5 Interconnected Systems 9.6 Slowly Varying Systems 9.7 Exercises 10 Perturbation Theory and Averaging 10.1 The Perturbation Method 10.2 Perturbation on the Infinite Interval 10.3 Periodic Perturbation of Autonomous Systems 10.4 Averaging 10.5 Weakly Nonlinear Second-Order Oscillators 10 6 General Averaging 10.7 Exercises 11 Singular Perturbations 11.1 The Standard Singular Perturbation Model 11.2 Time-Scale Properties of the Standard Model 11.3 Singular Perturbation on the Infinite Interval 11.4 Slow and Fast Manifolds 11.5 Stability Analysis 11.6 Exercises 12 Feedback Control 12.1 Control Problems 12.2 Stabilization via Linearization 12.3 Integral Control 12.4 Integral Control via Linearization 12.5 Gain Scheduling 12.6 Exercises 13 Feedback Linearization 13.1 Motivation 13.2 Input-Output Linearization 13.3 Full-State Linearization 13.4 State Feedback Control 13.4.1 Stabilization 13.4.2 Tracking 13.5 Exercises 14 Nonlinear Design Tools 14.1 Sliding Mode Control 14.1.1 Motivating Example 14.1.2 Stabilization 14.1.3 Tracking 14.1.4 Regulation via Integral Control 14.2 Lyapunov Redesign 14.2.1 Stabilization 14.2.2 Nonlinear Damping 14.3 Backstepping 14.4 Passivity-Based Control 14.5 High-Gain Observers 14.5.1 Motivating Example 14.5.2 Stabilization 14.5.3 Regulation via Integral Control 14.6 Exercises A Mathematical Review B Contraction Mapping C Proofs Note and References Bibliography Symbols Index