On Passivity Analysis and Passivation of Event-Triggered Feedback Systems Using Passivity Indices

While most of the work in the literature focuses on stability conditions for event-triggered systems, in this technical note we focus on passivity and passivation of event-triggered feedback interconnected systems of two input feed-forward output-feedback (IF-OF) passive systems. Passivity indices (levels) are used to measure the excess or shortage of passivity. It is shown that passivity indices (levels) of continuous feedback systems can be determined from passivity indices (levels) of individual subsystems. The passivation conditions to render a non-passive plant passive are also obtained based on passivity indices (levels). The results can be viewed as the extension of the well-known compositional property of passivity. Here we consider passivity in a unified event-triggered control scheme with event-triggered samplers located at both plant output and controller output. Under this scheme, we first derive the conditions to characterize passivity indices (levels) for the interconnected systems. The event-triggering condition proposed guarantees that these indices (levels) can be achieved. Then the passivation problem is considered and passivation conditions are provided. The passivation conditions depend on the passivity indices of the plant and controller and also the event-triggering condition, which reveals the trade off between desired passivity levels and communication resource utilization.