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Zeno hybrid systems
Author(s) -
Zhang Jun,
Johansson Karl Henrik,
Lygeros John,
Sastry Shankar
Publication year - 2001
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.592
Subject(s) - zeno's paradoxes , abstraction , quantum zeno effect , limit (mathematics) , set (abstract data type) , hybrid system , computer science , class (philosophy) , control theory (sociology) , mathematics , physics , mathematical analysis , artificial intelligence , quantum mechanics , open quantum system , control (management) , geometry , philosophy , epistemology , machine learning , quantum , programming language
The interacting continuous and discrete dynamics in hybrid systems may lead to Zeno executions, which are solutions of the system having infinitely many discrete transitions in finite time. Although physical systems do not show Zeno behaviour, models of real systems may be Zeno due to modelling abstraction. It is hard to analyse such models with the existing theory. Since abstraction is an important tool in the hierarchical design of hybrid systems, one would like to determine when it may lead to Zeno models. Zeno hybrid systems are studied in detail in the paper. Necessary and sufficient conditions for the existence of Zeno executions are given. The Zeno set is introduced as the ω limit set of a Zeno execution. Properties of the Zeno set are derived for a fairly large class of hybrid systems. Copyright 2001 © John Wiley & Sons, Ltd.