On the Sequence of Consecutive Matrix Powers of Boolean Matrices in
the Max-Plus Algebra
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, ISBN 981-02-3668-9, 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.
Downloads
- Corresponding technical report:
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Bibtex entry
@incollection{DeSDeM:98-20,
author={B. {D}e Schutter and B. {D}e Moor},
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={A. Tornamb\`e and G. Conte and A.M. Perdon},
publisher={Singapore: World Scientific},
pages={672--677},
year={1999}
}
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Last update: February 21, 2026.