The present work is concerned with the state-space formulation of the differential equations describing the dynamic behavior of systems modeled by a class of variable speed continuous PNs. Consequently, a qualitative property of systems, namely "stability" has been introduced. It has been shown that when all the eigenvalues of the evolution matrix of the state equation describing the continuous PN model have nonpositive real parts, the PN is stable. It is to be noted that a stable PN is a bounded PN. Then, It has been shown that a zero eigenvalue implies that the PN has a place-invariant and may be, as well, conservative. Properties concerning closed and open manufacturing lines have been proved. However, much work remains to be done. Properties such as transfer functions, controlability, and observability of this class of variable speed continuous Petri nets may be studied. We hope that this paper will stimulate further research in this area.
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