Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $55.93
Usually ships in 1-2 business days
(Save 34%)
Other sellers (Hardcover)
  • All (5) from $55.93   
  • New (5) from $55.93   

Overview

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms—algorithms that feature logic, timers, or combinations of digital and analog components.

With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms.

This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Read More Show Less

Editorial Reviews

Mathematical Reviews Clippings - Daniel Liberzon
The book is carefully written and contains many examples. It will be a good resource for both researchers already familiar with hybrid systems and those starting from scratch.
From the Publisher
"The book is carefully written and contains many examples. It will be a good resource for both researchers already familiar with hybrid systems and those starting from scratch."—Daniel Liberzon, Mathematical Reviews Clippings
Read More Show Less

Product Details

  • ISBN-13: 9780691153896
  • Publisher: Princeton University Press
  • Publication date: 3/18/2012
  • Edition description: New Edition
  • Pages: 232
  • Sales rank: 1,150,462
  • Product dimensions: 5.90 (w) x 9.30 (h) x 0.90 (d)

Meet the Author

Rafal Goebel is an assistant professor in the Department of Mathematics and Statistics at Loyola University, Chicago. Ricardo G. Sanfelice is an assistant professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona. Andrew R. Teel is a professor in the Electrical and Computer Engineering Department at the University of California, Santa Barbara.

Read More Show Less

Table of Contents

Preface ix

Chapter 1: Introduction 1
1.1 The modeling framework 1
1.2 Examples in science and engineering 2
1.3 Control system examples 7
1.4 Connections to other modeling frameworks 15
1.5 Notes 22

Chapter 2 The solution concept 25
2.1 Data of a hybrid system 25
2.2 Hybrid time domains and hybrid arcs 26
2.3 Solutions and their basic properties 29
2.4 Generators for classes of switching signals 35
2.5 Notes 41

Chapter 3 Uniform asymptotic stability, an initial treatment 43
3.1 Uniform global pre-asymptotic stability 43
3.2 Lyapunov functions 50
3.3 Relaxed Lyapunov conditions 60
3.4 Stability from containment 64
3.5 Equivalent characterizations 68
3.6 Notes 71

Chapter 4 Perturbations and generalized solutions 73
4.1 Differential and difference equations 73
4.2 Systems with state perturbations 76
4.3 Generalized solutions 79
4.4 Measurement noise in feedback control 84
4.5 Krasovskii solutions are Hermes solutions 88
4.6 Notes 94

Chapter 5 Preliminaries from set-valued analysis 97
5.1 Set convergence 97
5.2 Set-valued mappings 101
5.3 Graphical convergence of hybrid arcs 107
5.4 Differential inclusions 111
5.5 Notes 115

Chapter 6 Well-posed hybrid systems and their properties 117
6.1 Nominally well-posed hybrid systems 117
6.2 Basic assumptions on the data 120
6.3 Consequences of nominal well-posedness 125
6.4 Well-posed hybrid systems 132
6.5 Consequences of well-posedness 134
6.6 Notes 137

Chapter 7 Asymptotic stability, an in-depth treatment 139
7.1 Pre-asymptotic stability for nominally well-posed systems 141
7.2 Robustness concepts 148
7.3 Well-posed systems 151
7.4 Robustness corollaries 153
7.5 Smooth Lyapunov functions 156
7.6 Proof of robustness implies smooth Lyapunov functions 161
7.7 Notes 167

Chapter 8 Invariance principles 169
8.1 Invariance and ω-limits 169
8.2 Invariance principles involving Lyapunov-like functions 170
8.3 Stability analysis using invariance principles 176
8.4 Meagre-limsup invariance principles 178
8.5 Invariance principles for switching systems 181
8.6 Notes 184

Chapter 9 Conical approximation and asymptotic stability 185
9.1 Homogeneous hybrid systems 185
9.2 Homogeneity and perturbations 189
9.3 Conical approximation and stability 192
9.4 Notes 196

Appendix: List of Symbols 199
Bibliography 201
Index 211

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)