On the ultimate behavior of the sequence of consecutive powers of a matrix in the max-plus algebra Original Research Article

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.