In this paper, some tools for the analysis of a class of hybrid control systems for a continuous-time plant with input magnitude saturation are presented. We show that certain continuous-time LMI-based techniques can be extended to this setting when a dwell-time property is satisfied by the hybrid loop. Moreover, for the case in which the hybrid controller has the same order as the plant, the synthesis of a static direct linear anti-windup (DLAW) compensator is proposed. The need of including the flow and jump sets in the analysis and synthesis conditions leads to LMIs for global results, that is, when the plant is exponentially stable and BMIs otherwise.