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In this work, we present a new and effective method to design discrete-time static output-feedback H∞ controllers. This new method, based on a Linear Matrix Inequality (LMI) formulation, introduces a suitable transformation of the LMI variables that allows to obtain an explicit expression for the output-feedback gain matrix. Moreover, for problems involving a set of subsystems with information exchange constraints, a convenient structure on the LMI variables can be imposed in order to design semi-decentralized controllers, where the corresponding output-feedback gain matrix has a prescribed zero-nonzero structure. To illustrate the proposed methodology, discrete-time static velocity-feedback H∞ controllers to mitigate the seismic response of a five-story building are designed. In particular, two different designs are presented: (i) a centralized controller that requires all the inter-story velocities to compute the control actions, and (ii) a semi-decentralized controller that can operate using only the inter-story velocities of neighboring floors.