In: Proceedings of the 32nd Midwest Symposium on Circuits and Systems, 1989, Champaign, IL, USA, pages 161-164. Piscataway, NJ, USA: IEEE Service Center, 1990.
Abstract: Murata's state equation for standard Petri nets is extended to other continuous time systems. The crucial step in this development is to consider conceptually the marking's entries of a Petri net to be nonnegative real numbers rather than integers. This will allow the introduction of calculus into the state equation, which is a differential rather than linear equation. Murata's state equation is a finite difference approximation to this equation. The proposed state equation will be a stochastic differential equation if random time is associated with each transition.
Keywords: generalized state equation; stochastic differential equation.
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