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