Performance analysis in iterative feedback connection of passive systems

We propose a class of dissipative dynamical systems whose performance is strictly improved via feedback connection. The proposed class characterizes dissipative properties of the dynamical systems with two parameters. The parameters enable us to quantitatively evaluate the dissipation performance of the system by the H
_∞
norm. Assuming that two subsystems belong to the proposed class, we show that their feedback connection inherits the same class of the subsystem. The feedback connection is interpreted as the transition of the two parameters. In addition, it is further shown that the dissipation performance is strictly improved via feedback connection. Furthermore, we expand the feedback system to a large-scale system via iterative feedback connection of the dissipative subsystems. The dissipation performance of the entire system is gradually reinforced with the increase of the number of subsystems.