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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

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

Rafal Goebel

Ricardo G. Sanfelice

Andrew R. Teel

Princeton University Press

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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