Second order theory of min-linear systems and its application to discrete event systems
Guy Cohen, Stéphane Gaubert, Ramine Nikoukhah, Jean-Pierre Quadrat · 2002
A second-order theory for linear systems over the (min,+)-algebra is developed. In particular, the classical notion of correlation is extended to this algebraic structure. It turns out that if timed event graphs are modeled as linear systems in this algebra, this notion of correlation can be used to study stocks and sojourn times, and thus to characterize internal stability (boundedness of stocks and sojourn times). This theory relies heavily on the algebraic notion of residuation.>