Eigenvalues of Time-invariant Max-Min-Plus-Scaling Discrete-Event Systems

Reference

S. Markkassery, T. van den Boom, and B. De Schutter, "Eigenvalues of Time-invariant Max-Min-Plus-Scaling Discrete-Event Systems," Proceedings of the 2024 European Control Conference, Stockholm, Sweden, pp. 2017-2022, June 2024.

Abstract

This paper proposes an approach to find the eigenvalues and eigenvectors of a class of autonomous max-min-plus-scaling (MMPS) systems. First we show that time-invariant, monotone and non-expansive MMPS systems with only time variables has a unique structural eigenvalue and eigenvector under some conditions. Then, we propose a mixed-integer linear programming (MILP) algorithm to calculate the eigenvalue and the corresponding eigenvector for such systems. Finally, we present a modified linear programming (LP) algorithm to find all the eigenvalues of a general time-invariant MMPS system.

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Bibtex entry

@inproceedings{Marvan:24-017,
author={S. Markkassery and T. van den Boom and B. {D}e Schutter},
title={Eigenvalues of Time-invariant Max-Min-Plus-Scaling Discrete-Event Systems},
booktitle={Proceedings of the 2024 European Control Conference},
address={Stockholm, Sweden},
pages={2017--2022},
month=jun,
year={2024},
doi={10.23919/ECC64448.2024.10591257}
}

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