On the sequence of consecutive powers of a matrix in a Boolean algebra

Authors
De Schutter, B De Moor, B
Citation
B. De Schutter et B. De Moor, On the sequence of consecutive powers of a matrix in a Boolean algebra, SIAM J MATR, 21(1), 1999, pp. 328-354
Citations number
27
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN journal
08954798 → ACNP
Volume
21
Issue
1
Year of publication
1999
Pages
328 - 354
Database
ISI
SICI code
0895-4798(19991027)21:1<328:OTSOCP>2.0.ZU;2-X
Abstract
In this paper we consider the sequence of consecutive powers of a matrix in a Boolean algebra. We characterize the ultimate behavior of this sequence, we study the transient part of the sequence, and we derive upper bounds fo r the length of this transient part. We also indicate how these results can be used in the analysis of Markov chains and in max-plus algebraic system theory for discrete event systems.