Hybrid Dynamical Systems

Modeling, Stability, and Robustness

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

• Publisher: Princeton University Press
• Year: 2012
• Print ISBN: 9780691153896
• eBook ISBN: 9781400842636
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Half title
• Title
• Copyright
• Dedication
• Contents
• Preface
• 1 Introduction
• 2 The solution concept
• 3 Uniform asymptotic stability, an initial treatment
• 4 Perturbations and generalized solutions
• 5 Preliminaries from set-valued analysis
• 6 Well-posed hybrid systems and their properties
• 7 Asymptotic stability, an in-depth treatment
• 8 Invariance principles
• 9 Conical approximation and asymptotic stability
• Appendix: List of Symbols
• Bibliography
• Index