**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.

Corresponding technical report: pdf file (190 KB)

@incollection{DeSDeM:98-20,

author={B. {D}e Schutter and B. {D}e Moor},

title={On the sequence of consecutive matrix powers of boolean matrices in the max-plus algebra},

booktitle={Theory and Practice of Control and Systems \rm(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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