  We study the well-posedness of a class of dynamical flow network systems
describing the dynamical mass balance among a finite number of cells exchanging
flow of a commodity between themselves and with the external environment.
Systems in the considered class are described as differential inclusions
whereby the routing matrix is constant and the outflow from each cell in the
network is limited by a control that is a Lipschitz continuous function of the
state of the network. In many applications, such as queueing systems and
traffic signal control, it is common that an empty queue can be allowed to have
more outflow than the mass in the queue. While models for this scenario have
previously been presented for open-loop outflow controls, this result ensures
the existence and uniqueness of solutions for the network flow dynamics in the
case Lipschitz continuous feedback controllers.
