# Time-triggering versus event-triggering control over communication channels

## TL;DR

This paper compares time-triggered and event-triggered control strategies for stabilizing unstable plants over communication channels with unknown delays, revealing a critical delay threshold where information loss balances implicit information from event triggers.

## Contribution

It extends previous results by analyzing vector systems and comparing event-triggered control with time-triggered control under unknown delays, highlighting a critical delay threshold.

## Key findings

- Critical delay equals the inverse of the plant's entropy rate.
- Event triggering's implicit information is offset by communication delays.
- Extended data-rate theorem for time-triggered control with unknown delays.

## Abstract

Time-triggered and event-triggered control strategies for stabilization of an unstable plant over a rate-limited communication channel subject to unknown, bounded delay are studied and compared. Event triggering carries implicit information, revealing the state of the plant. However, the delay in the communication channel causes information loss, as it makes the state information out of date. There is a critical delay value, when the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events. This occurs when the maximum delay equals the inverse of the entropy rate of the plant. In this context, extensions of our previous results for event triggering strategies are presented for vector systems and are compared with the data-rate theorem for time-triggered control, that is extended here to a setting with unknown delay.