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Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 39, NO. 2, FEBRUARY 1994 269
Lyapunov Stability of a Class
of Discrete Event Systems
Kevin M. Passino, Member, IEEE, Anthony N.Michel, Fellow, IEEE, and Panos J. Antsaklis, Fellow, IEEE
Absh.acf-Discrete event systems (DES)are dynamical systems
which evolve in time by the occurrence of events at possibly
irregular time intervals. "Logical" DES are a class of discrete
time DES with equationsof motion that are most often nonliiear
and discontinuous with respect to event occurrences. Recently,
there has been much interest in studying the stability properties
of logical DES and several definitions for stability, and methods
for stability analysis have been proposed. Here we introduce
a logical DES model and define stability in the sense of Lya-
punov and asymptotic stability for logical DES. Then we show
that a more conventional analysis of stability which employs
appropriate Lyapunov functions can be used for logical DES.
We provide a general characterizationof the stability properties
of automata-theoretic DES models, Petri nets, and finite state
systems. Furthermore, the Lyapunov stability analysis approach
is illustrated on a manufacturing system that processes batchesof
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