Event-triggered stabilization of disturbed linear systems over digital channels

TL;DR

This paper develops an event-triggered control method for stabilizing linear systems over digital channels with delays and disturbances, identifying how delay impacts required transmission rates and the sufficiency of timing information.

Contribution

It introduces an encoding-decoding scheme and bounds on packet size and transmission rate for stabilization over delayed digital channels, highlighting the role of timing information.

Findings

Timing information suffices for stabilization at small delays.

Increased delay necessitates higher transmission rates.

Large delays require rates exceeding classic data-rate limits.

Abstract

We present an event-triggered control strategy for stabilizing a scalar, continuous-time, time-invariant, linear system over a digital communication channel having bounded delay, and in the presence of bounded system disturbance. We propose an encoding-decoding scheme, and determine lower bounds on the packet size and on the information transmission rate which are sufficient for stabilization. We show that for small values of the delay, the timing information implicit in the triggering events is enough to stabilize the system with any positive rate. In contrast, when the delay increases beyond a critical threshold, the timing information alone is not enough to stabilize the system and the transmission rate begins to increase. Finally, large values of the delay require transmission rates higher than what prescribed by the classic data-rate theorem. The results are numerically validated using a linearized model of an inverted pendulum.