# Local analysis of hybrid systems on polyhedral sets with state-dependent switching

• Volume: 24, Issue: 2, page 341-355
• ISSN: 1641-876X

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## Abstract

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This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.

## How to cite

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John Leth, and Rafael Wisniewski. "Local analysis of hybrid systems on polyhedral sets with state-dependent switching." International Journal of Applied Mathematics and Computer Science 24.2 (2014): 341-355. <http://eudml.org/doc/271865>.

@article{JohnLeth2014,
abstract = {This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.},
author = {John Leth, Rafael Wisniewski},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {stability; switched systems; hybrid systems; differential inclusions},
language = {eng},
number = {2},
pages = {341-355},
title = {Local analysis of hybrid systems on polyhedral sets with state-dependent switching},
url = {http://eudml.org/doc/271865},
volume = {24},
year = {2014},
}

TY - JOUR
AU - John Leth
AU - Rafael Wisniewski
TI - Local analysis of hybrid systems on polyhedral sets with state-dependent switching
JO - International Journal of Applied Mathematics and Computer Science
PY - 2014
VL - 24
IS - 2
SP - 341
EP - 355
AB - This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
LA - eng
KW - stability; switched systems; hybrid systems; differential inclusions
UR - http://eudml.org/doc/271865
ER -

## References

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