Abstract This work develops a unified modeling framework for piezoelectric structures controlled by passive shunts connected to a single transducer and/or networks interconnecting multiple transducers. A common tuning procedure for these different control approaches, termed decentralized and centralized approaches, respectively, is proposed. The generic model is then used to compare them in terms of vibration mitigation performance. It is shown that decentralization can be detrimental to performance in general. Digital vibration absorbers are then leveraged to realize the shunts and/or networks. In this regard, the proposed tuning procedure solely relies on characteristics that can be identified from the digital units of these absorbers. The theoretical developments are numerically and experimentally validated on piezoelectric beams.