Eigenvalues of dynamic max-min systems

Discrete event dynamic systems are studied in which the time evolution depends on the max-, min-, and the summation operation simultaneously. Specifically, necessary and sufficient conditions are given under which the operator which characterizes the evolution of such a system has an eigenvalue and eigenvector(s). Numerical algorithms to calculate these quantities are also provided.Most of the research described in this paper was done while at École des Mines de Paris in Fontainebleau, Centre d'Automatique et Informatique, France, during the summer of 1989.