Hybrid Dynamical Systems
Modeling, Stability, and Robustness
R. Goebel, R. G. Sanfelice, and A. R. Teel
Princeton University Press
Publisher's website: http://press.princeton.edu/titles/9759.html
Chapter 1 (sample): http://press.princeton.edu/chapters/s9759.pdf
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.
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.
Chapter 1: Introduction
Chapter 2: The solution concept
Chapter 3: Uniform asymptotic stability, an initial treatment
Chapter 4: Perturbations and generalized solutions
Chapter 5: Preliminaries from set-valued analysis
Chapter 6: Well-posed hybrid systems and their properties
Chapter 7: Asymptotic stability, an in-depth treatment
Chapter 8: Invariance principles
Chapter 9: Conical approximation and asymptotic stability