**Reference:**

B. De Schutter and
B. De Moor,
"The characteristic equation and minimal state space realization of
SISO systems in the max algebra," in *11th International Conference
on Analysis and Optimization of Systems *(Sophia-Antipolis,
France, June 1994) (G. Cohen and J.P. Quadrat, eds.), vol. 199 of
*Lecture Notes in Control and Information Sciences*, Springer,
ISBN 3-540-19896-2, pp. 273-282, 1994.

**Abstract:**

In this paper 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}. We use these results to develop a
procedure to find a minimal state space realization of a single input
single output (SISO) discrete event system in the max algebra, given
its Markov parameters.

Online version of the paper

Corresponding technical report: pdf file (153 KB)

@incollection{DeSDeM:93-57a,

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

title={The characteristic equation and minimal state space realization of {SISO} systems in the max algebra},

booktitle={11th International Conference on Analysis and Optimization of Systems \rm(Sophia-Antipolis, France, June 1994)},

series={Lecture Notes in Control and Information Sciences},

volume={199},

editor={G. Cohen and J.P. Quadrat},

publisher={Springer},

pages={273--282},

year={1994},

doi={10.1007/BFb0033557}

}

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