Abstract

A Second Order Theory is developed for linear systems over the (min, +)-algebra; in particular the classical notion of correlation is extended to this algebraic structure. It turns out that if we model timed event graphs as linear systems in this algebra, this new 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 which is briefly presented. 1 Introduction In [4, 6, 5], a linear system theory analogous to the conventional theory has been developed for a particular class of Discrete Event Dynamic Systems (DEDS) called Timed Event Graphs (TEG). This theory extends the notions of state space, impulse response and transfer function to TEG's. The periodic behavior of these systems has been characterized and a spectral theory has been developed. The key feature which allows extending all these classical concepts is a gene...

Citations

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