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.
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BibTeX
@inproceedings{LopKer:11-038,
author = {Lopes, Gabriel A. D. and Kersbergen, Bart and van den Boom, Ton
and De Schutter, Bart and Babu{\v{s}}ka, Robert},
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}
}