Many gene-regulatory networks necessarily display robust dynamics that are insensitive to noise and stable under evolution. We propose that a class of hybrid systems can be used to relate the structure of these networks to their dynamics and provide insight into the origin of robustness. In these systems, the genes are represented by logical functions, and the controlling transcription factor protein molecules are real variables, which are produced and destroyed. As the transcription factor concentrations cross thresholds, they control the production of other transcription factors. We discuss mathematical analysis of these systems and show how the concepts of robustness and minimality can be used to generate putative logical organizations based on observed symbolic sequences. We apply the methods to control of the cell cycle in yeast.