This paper considers the problem of stabilizing a linear time-invariant system in the presence of plant measurements that are available in an intermittent fashion. We propose a dynamic output feedback controller equipped with a holding device that is a linear time-invariant system whose state is reset when a new measure is available. We provide an LMI-based design procedure for the co-design of the dynamic controller and holding device parameters. Our approach relies on Lyapunov theory for hybrid systems and addresses the stability analysis in a way that is reminiscent of an "input- to-state stability small gain" philosophy. The effectiveness of the proposed LMI-based design is showcased in a numerical example.