A state-space model of a discharge air system (DAS) is developed. Simulation results obtained from the developed model compare well with the published experimental data. The optimal control strategies and optimal performance of DAS to step changes in setpoints are given for two cases: a heating case with temperature control, and a cooling case with temperature and humidity control. Results show that the outputs (discharge air temperature and humidity ratio) of the system reach the chosen setpoints rapidly and smoothly compared with that of PI control results published in the literature.