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, 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.
Publisher page
Downloads
Extended version
- 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, bibtex, report (pdf))
BibTeX
@incollection{DeSDeM:93-57a,
author = {De Schutter, Bart and De Moor, Bart},
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 \normalfont(Sophia-Antipolis, France, June 1994)},
series = {Lecture Notes in Control and Information Sciences},
volume = {199},
editor = {Cohen, Guy and Quadrat, Jean-Pierre},
publisher = {Springer},
pages = {273--282},
year = {1994}
}