Title :
Second order theory of min-linear systems and its application to discrete event systems
Author :
Cohen, G. ; Gaubert, Stephane ; Nikoukhah, R. ; Quadrat, J.
Author_Institution :
INRIA-Rocquencourt, Le Chesnay
Abstract :
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
Keywords :
Petri nets; algebra; correlation methods; discrete event simulation; discrete time systems; linear systems; (min,+)-algebra; boundedness; correlation; discrete event systems; internal stability; min-linear systems; residuation; second-order theory; sojourn times; stocks; timed event graphs; Algebra; Bars; Counting circuits; Discrete event systems; Equations; Linear systems; Stability; State-space methods; Stochastic processes;
Conference_Titel :
Decision and Control, 1991., Proceedings of the 30th IEEE Conference on
Conference_Location :
Brighton
Print_ISBN :
0-7803-0450-0
DOI :
10.1109/CDC.1991.261654
