Split range control design provides a stable and optimal operation for targeted temperatures, while the utility cost is minimized for all possible disturbance variations. An effective controller design named passivity concept is presented to regulate the stability of split range control of heat exchanger networks, in this work. The dynamic models of the proposed system are formulated in state space domain. These state space models of heat exchanger networks can represent both the process and the disturbance transfer functions. These transfer functions can determine whether the heat exchanger networks is passive or not by analyzing the passivity index. As a result, the split range control of heat exchanger networks is non-passive system. Therefore, the introduction of the weighting function is proposed to adapt the heat exchanger networks into strictly passive system. The passive controllers are then designed in order to keep the heat exchanger networks at the robust operation. The proposed method is tested and compared with PI controllers and illustrates that the passivity approach can give a better performance over conventional PI controllers. In addition, the dynamic responses of target temperature with passive controllers have a lower oscillation.