The paper presents an analysis of continuous Petri nets using linear algebra of matrices. It provides a link between the classical results of linear systems and Petri nets via the continuous model. A class of variable speed continuous Petri nets (VCPNs), namely Extended State Machines VCPNs (ESMVCPNs) is studied A state-variable representation and its associated matrix algebra are used to describe systems modeled by ESMVCPNs. The state variable formulation introduced here is that of a linear continuous time-invariant system with nonnegative state (marking) and control vector. The stability and asymptotic stability concepts of linear dynamic systems are applied to continuous Petri nets. A necessary and sufficient condition of conservativeness of ESMVCPNs, based on eigenvalues, is proved. These results are used for the control of a production system.
Continuous Petri Nets, State equation, Stability, Modeling, Control, Analysis, Eigenvalues, Production Systems.
All articles published by Studies in Informatics and Control (SIC) are published in accordance with the terms and conditions of the Creative Commons Attribution License (CC BY-NC-SA 4.0).