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.