Abstract:
In this paper we first present the exponential stability of discrete event
dynamic systems (DEDS) available in the literature. The result is then
applied to a class of discrete event systems modeled by Petri net. In
particular it is shown that a Petri net model of a discrete event system will be
exponentially stable if the transition firing obeys certain Lyapunov type
rules. In other words, the result obtained here shows that if the Petri net has a
given marking at a certain time and the firing of the transitions are done
according to certain rules and conditions then the marking of the system
states will eventually go to zero in an exponential manner. As a result the
finite capacity buffers in the system will not suffer any overflow. An
example is given at the end in order to give more insight to the results
obtained here.