Small and medium-size buildings employ a multi-distributed individual air-conditioning system that utilizes package air conditioners instead of centralized cooling systems, which can allow easier building management and maintenance, along with a diversification of facility use. Inverter driven system heat pumps have been developed to achieve not only an easy distribution control, allowing free combination of indoor units with different models and different capacities, but also wide applications to intelligent air conditioning. However, the control algorithms of the system heat pump are limited in the open literature, due to complicated operating conditions. In this paper, an inverter-driven system heat pump having two indoor units with electronic expansion valves (EEV) was simulated in the cooling mode. An integral optimum regulating controller employing the state space control method was also simulated, and applied to the system-heat pump system, to obtain efficient control of the MIMO (multi input multi output) system. The simulation model for the controller yielded satisfactory prediction results. The new control model can be successfully utilized as a basic tool in controller design.