A quasi-decentralized state estimation and control architecture for plants with limited state measurements and distributed, interconnected units that exchange information over a shared communication network is developed in this work. The objective is to stabilize the plant while minimizing unnecessary network resource utilization and communication costs. The networked control architecture is composed of a family of local control systems that transmit their data in a discrete (on/off) fashion over the network. Each control system includes a state observer that generates estimates of the local state variables from the measured outputs. The estimates are used to implement the local feedback control law and are also shared over the network with the control systems of the interconnected units to account for the interactions between the units. To reduce the exchange of information over the network as much as possible without sacrificing stability, dynamic models of the interconnected units are embedded in the local control system of each unit to provide it with an estimate of the evolution of its neighbors when data are not transmitted through the network. The state of each model is then updated using the state estimate generated by the observer of the corresponding unit and transmitted over the network when communication is re-established. An explicit characterization of the maximum allowable update period (i.e., minimum cross communication frequency between the distributed control systems) needed to enforce the desired stability and performance properties is obtained in terms of the plant model mismatch, controller, and observer design parameters. The design and implementation of the developed architecture are illustrated using a chemical plant example and compared with other possible networked control strategies. The comparison reveals that the lack of full state measurements imposes limitations on the maximum allowable update period, even if the models used to recreate the plant units' dynamics are accurate. It is also shown that the quasi-decentralized control architecture is more robust than a centralized networked control structure, with respect to communication suspension.