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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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Preliminaries from set-valued analysis

Preliminaries from set-valued analysis

Chapter:
(p.97) Chapter Five Preliminaries from set-valued analysis
Source:
Hybrid Dynamical Systems
Author(s):

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153896.003.0005

This chapter includes the necessary background on further developments in the theory of hybrid systems. It first presents the notion of convergence for a sequence of sets and how it generalizes the notion of convergence of a sequence of points. The chapter then deals with set-valued mappings and their continuity properties. Given a set-valued mapping M : ℝᵐ ⇉ ℝⁿ, the chapter defines the range of M as the set rgeM = {‎y ∈ ℝⁿ : Ǝx ∈ ℝᵐ such that yM(x)}‎; and the graph of M as the set gphM = {‎(x,y) ∈ ℝᵐ × ℝⁿ : yM(x)}‎. The chapter also specializes some of the concepts, such as graphical convergence, to hybrid arcs and provides further details in such a setting. Finally, the chapter discusses differential inclusions.

Keywords:   set-valued analysis, set-valued mappings, continuity properties, graphical convergence, differential inclusions, set convergence

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