In this work, a systematic strategy to design passive damping systems for structural vibration control is presented. The proposed design methodology is based on the equivalence between decentralized static velocity-feedback controllers and passive damping systems. By using recent developments in static output-feedback control, the design of passivedamping systems can be formulated as a single optimization problem with Linear Matrix Inequality constraints. Moreover, this optimization problem can be efficiently solved with standard numerical tools, even for large dimension systems. Due to its computational effectiveness, the proposed methodology can be applied to the design of passive damping systems for large structures. To illustrate the main ideas and methods, a passive damping system is designed for the seismic protection of a five-story building with excellent results.