Sampled-data H-infinity control of linear systems is considered. The measured output is sampled and the only restriction on the sampling is that the distance between sequel sampling times does not exceed a given bound. A novel performance index is introduced which takes into account the sampling rates of the measurement and it is thus related to the energy of the measurement noise. Three types of controllers are designed: a continuous-time controller, a sample and hold controller (synchronized with the sampling of the measurement), and an unsynchronized sampled and hold controller. A novel structure is adopted for these controllers where the dynamics of the controller is affected by the continuous-time state vector and the sampled value of this vector. A new approach, which was recently introduced to sampled-data stabilization is developed: the system is modeled as a continuous-time one, where the measurement output has a piecewise-continuous delay. A simple solution to the H-infinity control problem is derived in terms of linear matrix inequalities (LMIs). This solution is based on a new bounded real lemma (BRL) with state and disturbance delays. The results that are obtained for the output-feedback controller are readily applied to the problem of robust sampled-data H-infinity filtering with time-varying uncertain sampling rate. (C) 2007 Elsevier Ltd. All rights reserved.