Observer design for Continuous timed Petri Nets with product server semantics

This work deals with the observability problem in Continuous timed Petri Nets under the product semantics (PS-ContPN). The PS-ContPN is described by a non linear differential equation, where the non linearities come from the synchronization transitions. Regardless the marking non-negativeness, this work rewrites the PS-ContPN differential equation by splitting it into linear and non linear parts. Based on this representation, this paper uses two non linear control results to present two different observer design methodologies. The first methodology requires the non linear part to be dependent only on the PS-ContPN output, and the second one requires the non linear part to be Lipschitz.