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.

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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}
   }


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