Passivity of Cascaded Systems Based on The Analysis of Passivity Indices

Passivity index is defined in terms of an excess or shortage of passivity, and it has been introduced in order to extend the passivity-based stability conditions to the more general cases for both passive and non-passive systems. In this report, we revisit the secant criterion literature results from the perspective of passivity indices. While most of the passivity-based stability results in literature focus on studying the feedback interconnection of passive or non-passive systems, our results focus on the study of cascaded interconnection. In this report, we show how to use the secant criterion to quantify the excess/shortage of passivity for cascaded system which includes both passive and non-passive systems. We further show that under certain conditions, the cascaded interconnection can be directly stabilized via output feedback.