On the Eigenstructure of a Class of Max-Plus Linear Systems
Reference
G.A.D. Lopes,
B. Kersbergen,
T. van den Boom,
B. De Schutter, and
R. Babuška,
"On the Eigenstructure of a Class of Max-Plus Linear Systems," Proceedings of the 2011 50th IEEE Conference on Decision
and Control and European Control Conference (CDC-ECC), Orlando,
Florida, pp. 1823-1828, Dec. 2011.
Abstract
Various applications in scheduling, such as train timetables and
multi-legged locomotion, can be modeled using systems of max-plus
linear equations. In this framework, the eigenvalue of the system
matrix represents the total cycle time, whereas the eigenvector
dictates the steady state behavior. For a class of concurrent
two-state cyclic systems, with direct application to legged
locomotion, we present closed-form expressions for the eigenvalue and
eigenvector of the system matrix. Additionally, we probe into the
transient properties of this class of max-plus linear systems by
computing the coupling time.
Downloads
- Corresponding technical report:
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Bibtex entry
@inproceedings{LopKer:11-038,
author={G.A.D. Lopes and B. Kersbergen and T. van den Boom and B. {D}e Schutter
and R. Babu{\v{s}}ka},
title={On the Eigenstructure of a Class of Max-Plus Linear Systems},
booktitle={Proceedings of the 2011 50th IEEE Conference on Decision and Control
and European Control Conference (CDC-ECC)},
address={Orlando, Florida},
pages={1823--1828},
month=dec,
year={2011}
}
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