Nonlinear Control, 1st edition

Published by Pearson (January 27, 2014) © 2015

  • Hassan K. Khalil Michigan State University, East Lansing
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Access details

  • Instant access once purchased
  • Fulfilled by VitalSource
  • 180-day rental

Features

  • Add notes and highlights
  • Search by keyword or page

For a first course on nonlinear control that can be taught in one semester

 

This book emerges from the award-winning book, Nonlinear Systems, but has a distinctly different mission and organization. While Nonlinear Systems was intended as a reference and a text on nonlinear system analysis and its application to control, this streamlined book is intended as a text for a first course on nonlinear control. In Nonlinear Control, author Hassan K. Khalil employs a writing style that is intended to make the book accessible to a wider audience without compromising the rigor of the presentation.

 

Teaching and Learning Experience

This program will provide a better teaching and learning experience–for you and your students. It will help:

  • Provide an Accessible Approach to Nonlinear Control: This streamlined book is intended as a text for a first course on nonlinear control that can be taught in one semester.
  • Support Learning: Over 250 end-of-chapter exercises give students plenty of opportunities to put theory into action.

1 Introduction 1

1.1 Nonlinear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Nonlinear Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Overview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Two-Dimensional Systems 15

2.1 Qualitative Behavior of Linear Systems . . . . . . . . . . . . . . . . . . 17

2.2 Qualitative Behavior Near Equilibrium Points . . . . . . . . . . . . . . 21

2.3 Multiple Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Limit Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5 Numerical Construction of Phase Portraits . . . . . . . . . . . . . . . . 31

2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3 Stability of Equilibrium Points 37

3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3 Lyapunov’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.4 The Invariance Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5 Exponential Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.6 Region of Attraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.7 Converse Lyapunov Theorems . . . . . . . . . . . . . . . . . . . . . . . 68

3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4 Time-Varying and Perturbed Systems 75

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