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

被引：19
作者：
De Schutter, B
De Moor, B
机构：
[1] Delft Univ Technol, Fac Informat Technol & Syst, Lab Control Engn, NL-2600 GA Delft, Netherlands
[2] Katholieke Univ Leuven, ESAT, SISTA, B-3001 Heverlee, Belgium
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1999年 / 21卷 / 01期
关键词：
Boolean algebra; Boolean matrices; transient behavior; Markov chains; max-plus algebra;
D O I：
10.1137/S0895479897326079
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 for 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.
引用
收藏
页码：328 / 354
页数：27
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