Minimal state space realization of SISO systems in the max algebra

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

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 (401 KB)

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. (online paper, abstract, bibtex, tech. report (pdf))

@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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