A passivity measure of systems in cascade based on passivity indices

Passivity indices are defined in terms of an excess or shortage of passivity, and they have been introduced in order to extend the passivity-based stability conditions to more general cases for both passive and non-passive systems. While most of the work on passivity-based stability results in the literature focuses on employing the feedback interconnection of passive or non-passive systems, our results focus on a passivity measure for cascade interconnection. In this paper, we revisit the results on secant criterion from the perspective of passivity indices and we show how to use the secant criterion to measure the excess/shortage of passivity for cascaded Input Strictly Passive/Output Strictly Passive systems; we also propose a method to measure passivity for cascaded dissipative systems, where each subsystem could be passive or non-passive. Furthermore, we study the conditions under which the cascade interconnection can be directly stabilized via output feedback.