**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.

Corresponding technical report: pdf file (198 KB)

@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 \rm(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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