On min - max - plus systems , nonexpansive mappings and periodic solutions

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract Systems in which the operations min, max and addition appear simultaneously are called min-max-plus systems. Such systems, which are extensions of timed discrete event systems (which on their turn are based on the max-plus algebra, i.e. on the operations max and addition only), have been studied for some years now. An overview of various results, such as structural and nonstructural properties of min-max-plus systems and the existence of (structural) xed points for min-max-plus systems, will be given. Also a classiication of diierent kinds of min-max-plus systems is provided. Whereas the rst part of the paper deals with min-max-plus systems, the second part considers mainly systems characterized by nonexpansive mappings. For the latter class of systems, which encompasses the class of min-max-plus systems, some new results on the maximally possible period of periodic solutions are given.