The design of state observers and stabilising controllers for singularly perturbed discrete systems is studied in the paper. Noting the duality between the observer problem and the eigenvalue assignment problem, full-order observers are constructed by a systematic approach, which is based on time-scale decomposition concepts. By applying these results, stabilising problems for singularly perturbed discrete systems with inaccessible states are investigated. Finally, an application to a ninth-order boiler model is discussed.