**Reference:**

B. De Schutter and
B. De Moor,
"Minimal state space realization of SISO systems in the max algebra,"
Tech. rep. 93-57, ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 31 pp.,
Oct. 1993.

**Abstract:**

First we determine necessary and for some cases also sufficient
conditions for a polynomial to be the characteristic polynomial of a
matrix with elements in R_{max}. Then we indicate how to
construct a matrix such that its characteristic polynomial is equal to
a given monic polynomial in S_{max}, the extension of
R_{max}. Next we use these results to develop a procedure to
find the minimal state space realization of a single input single
output (SISO) discrete event system, given its Markov parameters.

Technical report: pdf file (283 KB)

@techreport{DeSDeM:93-57,

author={B. {D}e Schutter and B. {D}e Moor},

title={{Minimal} state space realization of {SISO} systems in the max algebra},

number={93-57},

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

address={Leuven, Belgium},

month=oct,

year={1993}

}

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