Performance Improvement via Iterative Connection of Passive Systems

This paper addresses model-set-based quantitative analysis of feedback systems. In particular, we find a model set describing the subsystems such that the performance improvement of the feedback system is achieved. To this end, we introduce the parameter-integrated passivity to accurately describe each passive subsystem and their feedback system. A model set describing passive systems is characterized by the two matrix parameters. The matrix parameters enable to evaluate the L_2-gain 'of the model set', which is defined as the L_2-gain of the worst-case system in the model set. With the parameter-integrated passivity, the quantitative analysis of a feedback system composed of two passive subsystems is provided as the parameter transition. Then, we find conditions on the matrix parameters to achieve the performance improvement such that the L_2-gain of the model set describing the feedback system is strictly less than that describing the subsystems. Subsequently, the performance improvement of the feedback system is extended to that of an iterative feedback system, which is a network system constructed by the feedback connection of multiple subsystems in a step-by-step manner. Then, we find conditions on the passivity parameters describing the baseline subsystem to achieve a gradual performance improvement with the subsystem connection.