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:


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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