Minimal (max,+) realization of convex sequences

Stéphane Gaubert; Peter Butkovič; Raymond Cuninghame-Green

doi:10.1137/S036301299528534X

Minimal (max,+) realization of convex sequences

Stéphane Gaubert
, Peter Butkovič
, Raymond Cuninghame-Green

University of Birmingham

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

45 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	137-147
Nombre de pages	11
journal	SIAM Journal on Control and Optimization
Volume	36
Numéro de publication	1
Les DOIs	https://doi.org/10.1137/S036301299528534X
état	Publié - 1 janv. 1998

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10.1137/S036301299528534X

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title = "Minimal (max,+) realization of convex sequences",

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.",

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AU - Cuninghame-Green, Raymond

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N2 - 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.

AB - 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.

KW - Discrete-event systems

KW - Max plus algebra

KW - Minimal realization

KW - Rational sequences

U2 - 10.1137/S036301299528534X

DO - 10.1137/S036301299528534X

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JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

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Minimal (max,+) realization of convex sequences

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