Nonlinear Systems, 3rd edition

Published by Pearson (December 18, 2001) © 2002

  • Hassan K. Khalil Michigan State University, East Lansing
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Title overview

For a first-year graduate-level course on nonlinear systems. It may also be used for self-study or reference by engineers and applied mathematicians.

The text is written to build the level of mathematical sophistication from chapter to chapter. It has been reorganized into four parts: Basic analysis, Analysis of feedback systems, Advanced analysis, and Nonlinear feedback control.

Table of contents

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
  • Continuous 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
  • L2 Gain
  • Feedback Systems: The Small-Gain Theorem

6. Passivity

  • Memoryless Functions
  • State Models
  • Positive Real Transfer Functions
  • L2 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

APPENDICES

  • A. Mathematical Review
  • B. Contraction Mapping
  • C. Proofs.
  • Notes and References

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