Previous work has identified that non-linear variables calculated from respiratory data vary between sleep states, and that variables derived from the non-linear analytical tool recurrence quantification analysis (RQA) are accurate infant sleep state discriminators. This study aims to apply these discriminators to automatically classify 30 s epochs of infant sleep as REM, non-REM and wake. Polysomnograms were obtained from 25 healthy infants at 2 weeks, 3, 6 and 12 months of age, and manually sleep staged as wake, REM and non-REM. Inter-breath interval data were extracted from the respiratory inductive plethysmograph, and RQA applied to calculate radius, determinism and laminarity. Time-series statistic and spectral analysis variables were also calculated. A nested cross-validation method was used to identify the optimal feature subset, and to train and evaluate a linear discriminant analysis-based classifier. The RQA features radius and laminarity and were reliably selected. Mean agreement was 79.7, 84.9, 84.0 and 79.2 % at 2 weeks, 3, 6 and 12 months, and the classifier performed better than a comparison classifier not including RQA variables. The performance of this sleep-staging tool compares favourably with inter-human agreement rates, and improves upon previous systems using only respiratory data. Applications include diagnostic screening and population-based sleep research.