Two H∞-based control strategies are proposed for application to civil engineering structures. The first strategy deals with a class of excitations with a specified ‘energy’ bound (H∞B-EB), whereas the second strategy addresses a class of excitations with a specified peak bound (H∞B-PB). Both control strategies are derived by minimizing an upper bound of the H∞ performance (i.e. energy or L2 gain) with the constraints (or penalties) on the peak values of another set of quantities, such as the control resources. These control strategies are formulated within the framework of linear matrix inequalities (LMIs), so that the LMI toolbox in MATLAB can be used effectively and conveniently. These control techniques are applied to a wind-excited 76-storey benchmark building and a long-span cable-stayed benchmark bridge subject to earthquakes to illustrate their effectiveness for practical problems, such as control of civil engineering structures. Copyright © 2004 John Wiley & Sons, Ltd.