Eigenvalues of Time-invariant Max-Min-Plus-Scaling Discrete-Event Systems
S. Markkassery (TU Delft - Team Ton van den Boom)
A.J.J. Van Den Boom (TU Delft - Team Ton van den Boom)
B De Schutter (TU Delft - Delft Center for Systems and Control)
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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.