We propose a class of dynamical systems that enables us to quantitatively evaluate dissipation performance in addition to expressing qualitative dissipative properties. Assuming that two subsystems belong to the proposed class, we show that the dissipation performance is strictly improved via feedback connection. We construct a larger-scale system via recursive feedback connection of the dissipate subsystems. Then, the performance of the entire network system is gradually reinforced with the increase of the number of subsystems. Ultimately, the output of the system cannot be driven by any disturbance input.