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Nonlinear Control, 1st edition

  • Hassan K. Khalil

Published by Pearson (February 6th 2014) - Copyright © 2015

1st edition

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Nonlinear Control

ISBN-13: 9780133499261

Includes: Hardcover
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$165.32 $206.65

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  • Hardcover

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Overview

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 that can be taught in one semester. 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. KEY TOPICS: Two-Dimensional Systems; Stability of Equilibrium Points; Time-Varying and Perturbed Systems; Passivity; Input-Output Stability; Stability of Feedback Systems; Special Nonlinear Forms; State Feedback Stabilization; Robust State Feedback Stabilization; Output Feedback Stabilization; Tracking and Regulation. MARKET: A useful introduction to nonlinear control.

Table of contents

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

4.1 Time-varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2 Perturbed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.3 Boundedness and Ultimate Boundedness . . . . . . . . . . . . . . . . . 85

4.4 Input-to-State Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5 Passivity 103

5.1 Memoryless Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.2 State Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.3 Positive Real Transfer Functions . . . . . . . . . . . . . . . . . . . . . 112

5.4 Connection with Lyapunov Stability . . . . . . . . . . . . . . . . . . . 115

5.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6 Input-Output Stability 121

6.1 L Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.2 L Stability of State Models . . . . . . . . . . . . . . . . . . . . . . . . 127

6.3 L2 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7 Stability of Feedback Systems

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