**Reference:**

B. De Schutter,
"On the ultimate behavior of the sequence of consecutive powers of a
matrix in the max-plus algebra," *Linear Algebra and Its
Applications*, vol. 307, no. 1-3, pp. 103-117, Mar. 2000.

**Abstract:**

We study the sequence of consecutive powers of a matrix in the
max-plus algebra, which has maximum and addition as its basic
operations. If the matrix is irreducible then it is well known that
the ultimate behavior of the sequence is cyclic. For reducible
matrices the ultimate behavior is more complex, but it is also cyclic
in nature. We will give a detailed characterization of the rates and
periods of the ultimate behavior for a general matrix.

Online version of the paper

Corresponding technical report: pdf file (207 KB)

@article{DeS:99-08,

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

title={On the ultimate behavior of the sequence of consecutive powers of a matrix in the max-plus algebra},

journal={Linear Algebra and Its Applications},

volume={307},

number={1--3},

pages={103--117},

month=mar,

year={2000},

doi={10.1016/S0024-3795(00)00013-6}

}

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