State equation and stability of a class of continuous Petri nets. Application to manufacturing lines

Continuous Petri nets (continuous PNs) have been defined by David and Alla to answer some modeling problems of continuous systems which cannot be modeled by discrete PNs or discrete event systems when the number of tokens becomes too large. The continuous approach of this modeling tool allows an analytical representation of these systems. Indeed, the marking of places and the instantaneous firing speeds of transitions are given by a set of differential equations. The modeling of a physical system is, generally, followed by a mathematical-equation description of the model. Our contribution is mainly based on the state-space formulation of the equations describing the dynamic behavior of systems modeled by continuous PNs. Consequently, a qualitative property of systems, namely “stability” is introduced. Properties relative to manufacturing lines are, as well, presented. General properties of systems, such as stability, place-invariant, and conservativeness are presented