Weak boundedness of timed continuous Petri nets

The paper presents the concepts of weak boundeness and weak conservativeness for general timed continuous Petri nets with infinite server semantics. Based on the reduction technique and the linear algebra of matrices, a timed continuous Petri net with joins can be transformed to a join-free type with the equivalent dynamics of their markings. We endeavor to improve the link between piecewise linear systems, timed continuous Petri nets, and dynamics properties. The weak boundeness and weak conservativeness of the type nets are characterized by the inequalities of the matrix measure that defines the dynamics properties of the markings.