The paper is focused on the case study of the advanced control of the heat exchanger network (HEN). The HEN is used for cooling petroleum produced by distillation. The robust model predictive control (RMPC) strategy is implemented to find the optimal control actions taking into account the boundaries on the control inputs. RMPC approach is also able to design the controller managing the process uncertainties. The aim is to demonstrate that the HEN robust model predictive control can be improved and the energy efficiency can be optimized using the parameter-dependent Lyapunov functions (PDLF). The simulation results confirmed also the energy savings.