Second order theory of min-linear systems and its application to discrete event systems

Guy Cohen; Stephane Gaubert; Ramine Nikoukhah; Jean Pierre Quadrat

Second order theory of min-linear systems and its application to discrete event systems

Guy Cohen, Stephane Gaubert, Ramine Nikoukhah, Jean Pierre Quadrat

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

36 Scopus citations

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.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Publisher	Institute of Electrical and Electronics Engineers
Pages	1511-1516
Number of pages	6
ISBN (Print)	0780304500
State	Published - 1 Dec 1991
Externally published	Yes
Event	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl Duration: 11 Dec 1991 → 13 Dec 1991

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2
ISSN (Print)	0191-2216

Conference

Conference	Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)
City	Brighton, Engl
Period	11/12/91 → 13/12/91

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Cite this

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title = "Second order theory of min-linear systems and its application to discrete event systems",

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.",

author = "Guy Cohen and Stephane Gaubert and Ramine Nikoukhah and Quadrat, {Jean Pierre}",

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series = "Proceedings of the IEEE Conference on Decision and Control",

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Cohen, G, Gaubert, S, Nikoukhah, R & Quadrat, JP 1991, Second order theory of min-linear systems and its application to discrete event systems. in Proceedings of the IEEE Conference on Decision and Control. Proceedings of the IEEE Conference on Decision and Control, vol. 2, Institute of Electrical and Electronics Engineers, pp. 1511-1516, Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3), Brighton, Engl, 11/12/91.

Second order theory of min-linear systems and its application to discrete event systems. / Cohen, Guy; Gaubert, Stephane; Nikoukhah, Ramine et al.
Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers, 1991. p. 1511-1516 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Y1 - 1991/12/1

N2 - 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.

AB - 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.

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Second order theory of min-linear systems and its application to discrete event systems

Abstract

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ASJC Scopus subject areas

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