MM functions, formed by finite composition of the operators min, max and translation, represent discrete-event systems involving disjunction, conjunction and delay. The paper shows how they may be formulated as homogeneous rational algebraic functions of degree one, over (max, +) algebra, and reviews the properties of such homogeneous functions, illustrated by some orbit-stability problems.

This paper discusses the properties of reachability and observability for linear systems over the max-plus algebra. Working in the event-domain, the concept of asticity is used to develop conditions for weak reachability and weak observability. In the reachability problem, residuation is used to determine if a state is reachable and to generate the required control sequence to reach it. In the observability problem, residuation is used to estimate the state. Finally, as in the continuous-variable...