Reference
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.
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.
Downloads
Original paper
- 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, pp. 273-282, 1994. (online paper, abstract, bibtex, tech. report (pdf))
BibTeX
@techreport{DeSDeM:93-57,
author = {De Schutter, Bart and De Moor, Bart},
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}
}