Minimal (max,+) Realization of Convex Sequences

Authors:
Stéphane Gaubert;Peter Butkovic;Raymond Cuninghame-Green
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1998

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Abstract

We show that the minimal dimension of a linear realization over the (max,+) semiring of a convex sequence is equal to the minimal size of a decomposition of the sequence as a supremum of discrete affine maps. The minimal-dimensional realization of any convex realizable sequence can thus be found in linear time. The result is based on a bound in terms of minors of the Hankel matrix.