Reference
B. De Schutter and B. De Moor, "Minimal realization in the max algebra," Tech.
report 94-29, ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 29 pp., May 1994.
Abstract
The main topic of this paper is the minimal realization problem in the max
algebra, which is one of the modeling frameworks that can be used to model
discrete event systems. First we determine necessary and for some cases also
sufficient conditions for a polynomial to be the characteristic polynomial of a
matrix in the max algebra. Then we show how a system of multivariate
max-algebraic polynomial equalities can be transformed into an Extended Linear
Complementarity Problem (ELCP). Finally we combine these results 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.
Downloads
BibTeX
@techreport{DeSDeM:94-29,
author = {De Schutter, Bart and De Moor, Bart},
title = {Minimal Realization in the Max Algebra},
number = {94-29},
institution = {ESAT-SISTA, K.U.Leuven},
address = {Leuven, Belgium},
month = may,
year = {1994}
}