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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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Conical approximation and asymptotic stability

Conical approximation and asymptotic stability

Chapter:
(p.185) Chapter Nine Conical approximation and asymptotic stability
Source:
Hybrid Dynamical Systems
Author(s):

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153896.003.0009

This chapter presents a technique of approximating a hybrid system with a conical hybrid system: a system with conical flow and jump sets and with constant or linear flow and jump maps. The main result here deduces pre-asymptotic stability for the original system from pre-asymptotic stability for the conical approximation. This result generalizes, to a hybrid system, the result that asymptotic stability for the linearization of a differential equation implies asymptotic stability for the differential equation. In many cases, the analysis of the conical approximation is simpler than of the original hybrid system; this is illustrated in several examples later in the chapter.

Keywords:   conical approximation, asymptotic stability, conical hybrid system, pre-asymptotic stability, differential equations, hybrid system

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