TITLE:
The Relation between the Stabilization Problem for Discrete Event Systems Modeled with Timed Petri Nets via Lyapunov Methods and Max-Plus Algebra
AUTHORS:
Zvi Retchkiman Konigsberg
KEYWORDS:
Discrete Event Systems, Lyapunov Methods, Max-Plus Algebra, Timed Petri Nets
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.7,
July
14,
2015
ABSTRACT: A discrete event system is a dynamical
system whose state evolves in time by the occurrence of events at possibly irregular
time intervals. Timed Petri nets are a graphical and mathematical modeling tool
applicable to discrete event systems in order to represent its states evolution
where the timing at which the state changes is taken into consideration. One of
the most important performance issues to be considered in a discrete event
system is its stability. Lyapunov theory provides the required tools needed to
aboard the stability and stabilization problems for discrete event systems
modeled with timed Petri nets whose mathematical model is given in terms of difference
equations. By proving stability one guarantees a bound on the discrete event
systems state dynamics. When the system is unstable, a sufficient condition to
stabilize the system is given. It is shown that it is possible to restrict the
discrete event systems state space in such a way that boundedness is achieved.
However, the restriction is not numerically precisely known. This inconvenience
is overcome by considering a specific recurrence equation, in the max-plus
algebra, which is assigned to the timed Petri net graphical model.