Abstract
The asymptotic behaviour of an algorithm in max algebra is discussed. It can be seen as an extension of the concept of periodicity which has been treated in max-algebra literature. The main result is that the asymptotic behaviour of the algorithm is characterized by one or more critical circuits in a generalized sense, and that two cases can be distinguished. In the first case the generalized critical circuit has length two, and generalized order-2 periodicity is found. In the second case the generalized critical circuits are of length one, and generalized order-1 periodicity is stated. Only the case of 2 × 2-matrices is treated. The treatment of this specific case leads to the formulation of a more general set-up in which square matrices of any size can be included. The notion of generalized critical circuit is introduced.
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© 1993 Birkhäuser Verlag Basel
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Braker, J.G., Resing, J.A.C. (1993). On a Generalized Asymptoticity Problem in Max Algebra. In: Balemi, S., Kozák, P., Smedinga, R. (eds) Discrete Event Systems: Modeling and Control. Progress in Systems and Control Theory, vol 13. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9120-2_10
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DOI: https://doi.org/10.1007/978-3-0348-9120-2_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9916-1
Online ISBN: 978-3-0348-9120-2
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