The Extended Linear Complementarity Problem and the Modeling and
Analysis of Hybrid Systems
Reference
B. De Schutter and
B. De Moor,
"The Extended Linear Complementarity Problem and the Modeling and
Analysis of Hybrid Systems," in Hybrid Systems V
(Proceedings of the 5th International Hybrid Systems Workshop,
Notre Dame, Indiana, Sept. 1997) (P. Antsaklis, W. Kohn, M. Lemmon, A.
Nerode, and S. Sastry, eds.), vol. 1567 of Lecture
Notes in Computer Science, Springer, ISBN 3-540-65643-X, pp.
70-85, 1999.
Abstract
First we give a short description of the Extended Linear
Complementarity Problem (ELCP), which is a mathematical programming
problem. We briefly discuss how this problem can be used in the
analysis of discrete event systems and continuous variable systems.
Next we show that the ELCP can also be used to model and to analyze
hybrid systems. More specifically, we consider a
traffic-light-controlled intersection, which can be considered as a
hybrid system. We construct a model that describes the evolution of
the queue lengths in the various lanes (as continuous variables) as a
function of time and we show that this leads to an ELCP. Furthermore,
it can be shown that some problems in the analysis of another class of
hybrid systems, the "complementary-slackness systems", also lead to an
ELCP.
Downloads
- Corresponding technical report:
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Bibtex entry
@incollection{DeSDeM:98-40,
author={B. {D}e Schutter and B. {D}e Moor},
title={The Extended Linear Complementarity Problem and the Modeling and Analysis
of Hybrid Systems},
booktitle={Hybrid Systems V \normalfont(Proceedings of the 5th International
Hybrid Systems Workshop, Notre Dame, Indiana, Sept. 1997)},
series={Lecture Notes in Computer Science},
volume={1567},
editor={P. Antsaklis and W. Kohn and M. Lemmon and A. Nerode and S. Sastry},
publisher={Springer},
pages={70--85},
year={1999}
}
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Last update: February 21, 2026.