Hybrid Dynamical Systems

Rafal Goebel; Ricardo G. Sanfelice; Andrew R. Teel

Rafal Goebel, Ricardo G. Sanfelice and Andrew R. Teel

Hybrid Dynamical Systems

Modeling, Stability, and Robustness

Princeton University Press | 2012

https://doi.org/10.1515/9781400842636

Overview
Contents

About this book

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.

Author information

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.

Reviews

The book presents a clean and self-contained exposition of hybrid systems, starting from the elementary definitions, continuing with the basic tools and finishing with more recent contributions in the literature.---Marco Castrillon Lopez, European Mathematical Society

"This superb book unifies some of the key developments in hybrid dynamical systems from the last decade and, through elegant and clear technical content, introduces the necessary tools for understanding the stability of these systems. It will be a great resource for graduate students and researchers in the field."—Magnus Egerstedt, Georgia Institute of Technology

"With broad applications for science and engineering, this first-rate book develops solid foundations for a comprehensive theory of hybrid dynamical systems. Diverse literature is brought together for the first time, making a huge body of knowledge conveniently accessible."—Dennis S. Bernstein, University of Michigan

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

Frontmatter Free access PDF PDF	i
Contents Free access PDF PDF	vii
Preface Access restricted Content is available PDF PDF	ix
Chapter One. Introduction Access restricted Content is available PDF PDF	1
Chapter Two. The solution concept Access restricted Content is available PDF PDF	25
Chapter Three. Uniform asymptotic stability, an initial treatment Access restricted Content is available PDF PDF	43
Chapter Four. Perturbations and generalized solutions Access restricted Content is available PDF PDF	73
Chapter Five. Preliminaries from set-valued analysis Access restricted Content is available PDF PDF	97
Chapter Six. Well-posed hybrid systems and their properties Access restricted Content is available PDF PDF	117
Chapter Seven. Asymptotic stability, an in-depth treatment Access restricted Content is available PDF PDF	139
Chapter Eight. Invariance principles Access restricted Content is available PDF PDF	169
Chapter Nine. Conical approximation and asymptotic stability Access restricted Content is available PDF PDF	185
Appendix: List of Symbols Access restricted Content is available PDF PDF	199
Bibliography Access restricted Content is available PDF PDF	201
Index Access restricted Content is available PDF PDF	211

(Deutsch)

Hybrid Dynamical Systems

Modeling, Stability, and Robustness

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