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. Babuska, "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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Corresponding technical report: pdf file (123 KB)
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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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