**Reference:**

B. De Schutter and
B. De Moor,
"Minimal realization in the max algebra is an extended linear
complementarity problem," Tech. rep. 93-70, ESAT-SISTA, K.U.Leuven,
Leuven, Belgium, 18 pp., Dec. 1993.

**Abstract:**

In this paper we demonstrate that the minimal state space realization
problem in the max algebra can be transformed into an Extended Linear
Complementarity Problem (ELCP). We use an algorithm that finds all
solutions of an ELCP to find all equivalent minimal state space
realizations of a single input single output (SISO) discrete event
system. We also give a geometrical description of the set of all
minimal realizations of a SISO max-linear discrete event system.

Technical report: pdf file (215 KB)

@techreport{DeSDeM:93-70,

author={B. {De Schutter} and B. {De Moor}},

title={{Minimal} realization in the max algebra is an extended linear complementarity problem},

number={93-70},

institution={ESAT-SISTA, K.U.Leuven},

address={Leuven, Belgium},

month=dec,

year={1993}

}

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