Reference
B. De Schutter and B. De Moor, "On the sequence of consecutive matrix powers of
Boolean matrices in the max-plus algebra," in
Theory and
Practice of Control and Systems (Proceedings of the 6th IEEE
Mediterranean Conference on Control and Systems, Alghero, Italy, June 1998) (A.
Tornambè, G. Conte, and
A. M.
Perdon, eds.), Singapore: World Scientific, pp. 672-677, 1999.
Abstract
In this paper we consider sequences of consecutive powers of boolean matrices
in the max-plus algebra, which is one of the frameworks that can be used to
model certain classes of discrete event systems. The ultimate behavior of a
sequence of consecutive max-plus-algebraic powers of a boolean matrix is
cyclic. First we derive upper bounds for the length of the cycles as a function
of the size of the matrix. Then we study the transient part of the sequence of
consecutive powers of a max-plus-algebraic boolean matrix, and we derive upper
bounds for the length of this transient part. These results can then be used in
the max-plus-algebraic system theory for discrete event systems.
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BibTeX
@incollection{DeSDeM:98-20,
author = {De Schutter, Bart and De Moor, Bart},
title = {On the Sequence of Consecutive Matrix Powers of {B}oolean
Matrices in the Max-Plus Algebra},
booktitle = {Theory and Practice of Control and Systems
\normalfont(Proceedings of the 6th IEEE Mediterranean
Conference on Control and Systems, Alghero, Italy, June 1998)},
editor = {Tornamb\`{e}, Antonio and Conte, Giuseppe and Perdon, Anna
Maria},
publisher = {Singapore: World Scientific},
pages = {672--677},
year = {1999}
}