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Hybrid Dynamical SystemsModeling, Stability, and Robustness$
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Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

Print publication date: 2012

Print ISBN-13: 9780691153896

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153896.001.0001

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(p.1) Chapter One Introduction
Hybrid Dynamical Systems

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Princeton University Press

This chapter presents the model of a hybrid system to be used in this volume. The focus is on the data structure and on modeling. The model suggests that the flow set, the flow map, the jump set, and the jump map can be specialized to capture the dynamics of purely continuous-time or discrete-time systems on ℝn. The former corresponds to a flow set equal to ℝn and an empty jump set, while the latter can be captured with an empty flow set and a jump set defined as ℝn. In addition, several examples of hybrid systems are given, including models of hybrid control systems. The model of a hybrid system is then related to other modeling frameworks; such as hybrid automata, impulsive differential equations, and switching systems.

Keywords:   hybrid system, data structure, modeling, flow set, flow map, jump set, jump map, continuous-time systems, discrete-time systems, modeling frameworks

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