A Class of Dynamical systems that Self-Reinforces the Dissipation Performance via Feedback Connection: Performance integrated Passivity Theorem

Abstract

We propose a class of dissipative dynamical systems whose performance is strictly improved via feedback connection. The proposed class characterizes the dissipative properties of the dynamical systems by two parameters. The parameters enable us to quantitatively evaluate the dissipation performance of the system by the L₂ gain. Assuming that two subsystems belong to the proposed class, we show that their feedback connection inherits the same class of the subsystems. 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.