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State quation and Stability for a Class of Continuous Petri Nets. Application to the Control of a Production Systems.

Chérif, Amer-Yahia; Noureddine, Zerhouni

In: Studies in Informatics and Control, Vol. 10, No. 4, pages 301-317. December 2001.

Abstract: 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 Continous 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.

Keywords: Continuous Petri Nets; State Equation; Stability; Modeling; Control; Analysis; Eigenvalues; Production Systems..

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