An active control system in civil engineering is a structure that mitigates the effect of external forces such as winds and earthquakes by applying counteracting control forces. Although they are able to adapt for a broad spectrum of conditions and structures, they involve significant increases in costs due to hardware such as actuators, sensors, and communication devices. There is a need of control strategies that lead to not only safe but also economical designs that take into account the physical structural properties of the system. In this paper we use the concept of structural sparsity to propose a mathematical framework for the design of control strategies that involve less information to compute a control action, considering prior information about the inherent structural relations between the components of the system to be controlled. We formulate the control design process as the solution of an optimization problem driven by a component associated with the performance of the controlled civil structure along with a norm that is built to induce structural sparsity in the parameters of the controller. As a study case of the proposed control design strategy we consider the model of a structure with magnetorheological (MR) dampers whose action is determined by a state feedback controller. The criterion used to design the parameters of the controller is the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm along with a structural sparsity-inducing norm that is built to encode the relations within and between stories through a hierarchical configuration. Simulations show that the resulting controller is able to reduce the story drift with a performance close to that of a non-sparse controller, requiring less information to compute the control action, and keeping physical consistency of the controlled system.