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Synchronization and Linearity: An Algebra for Discrete Event Systems
This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints, which is shown to parallel the classical linear system theory in several ways.
Algebraic tools for the performance evaluation of discrete event systems
It is shown that a certain class of Petri nets called event graphs can be represented as linear time-invariant finite-dimensional systems using some particular algebras. This sets the ground on which…
A linear-system-theoretic view of discrete-event processes
- G. Cohen, D. Dubois, J. Quadrat, M. Viot
- Computer Science, MathematicsThe 22nd IEEE Conference on Decision and Control
- 1 December 1983
An analogy between linear systems and a class of discrete-event systems is developed that can be viewed as linear, in the sense of an appropriate algebra, and the potentiality of this approach for the performance evaluation of repetitive production processes is illustrated.
Duality and separation theorems in idempotent semimodules
Numerical Computation of Spectral Elements in Max-Plus Algebra☆
Max-Plus Algebra and System Theory: Where We Are and Where to Go Now
Timed-event graphs with multipliers and homogeneous min-plus systems
The authors give a necessary and sufficient condition under which a fluid timed-event graph with multipliers can be reduced to a fluidtimed event graph without multipliers.
Linear system theory for discrete event systems
- G. Cohen, P. Moller, J. Quadrat, M. Viot
- Mathematics, Computer ScienceThe 23rd IEEE Conference on Decision and Control
- 1 December 1984
This paper first defines the particular class of timed Petri nets that can be described by "linear" recurrent equations and then develops concepts such as transfer matrix representations of such systems, stability, observability, controllability, feed-back stabilization, realization of transfer matrices etc...
Linear systems in (max, +) algebra
- M. Akian, G. Cohen, S. Gaubert, R. Nikoukhah, J. Quadrat
- Mathematics29th IEEE Conference on Decision and Control
- 5 December 1990
The general system of linear equations in the (max, +) algebra is studied. A symmetrization of this algebra and a new notion called balance which generalizes classical equations are introduced. This…
Idempotency: Algebraic system analysis of timed Petri nets
It is shown that Continuous Timed Petri Nets (CTPN) can be modeled by generalized polynomial recurrent equations in the (min,+) semiring and a correspondence between CTPN and Markov decision processes is established.