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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

(p.185) Chapter Nine Conical approximation and asymptotic stability
Hybrid Dynamical Systems

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Princeton University Press

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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