Passivity analysis and passivation of feedback systems using passivity indices

Passivity indices are used to measure the excess or shortage of passivity. While most of the work in the literature focuses on stability conditions for interconnected systems using passivity indices, here we focus on passivity and passivation of the feedback interconnection of two input feed-forward output-feedback (IF-OF) passive systems. The conditions are given to determine passivity indices in feedback interconnected systems. The results can be viewed as the extension of the well-known compositional property of passivity. We also consider the passivation problem which can be used to render a non-passive plant passive using a feedback interconnected passive controller. The passivity indices of the passivated system are also determined. The results derived do not require linearity of the systems as it is commonly assumed in the literature.