On the boundedness of timed continuous Petri nets

For a timed continuous Petri net (TCPN), the paper introduces a new concept of boundedness based on the existence of (positive) invariant sets with respect to the marking of the net, sets that are defined by weighted Hölder p-norms. For join-free TCPNs, this type of boundedness is characterized by inequalities satisfied by the measure of the matrix that defines the dynamics of the marking. Some connections with the structural properties of the net topology are also delivered.