Event-Triggered Stabilization of Linear Systems Under Bounded Bit Rates

TL;DR

This paper develops event-triggered control strategies for linear systems that ensure exponential practical stabilization under bounded communication bit rates, balancing transmission frequency and data precision.

Contribution

It introduces a novel approach to stabilize linear systems with bounded data rates using event-triggered control, ensuring stability and bounded transmission intervals.

Findings

Exponential practical stabilization achieved under bounded bit rates.

Guaranteed positive lower bounds on transmission and reception intervals.

Characterization of the necessary and sufficient average data rate.

Abstract

This paper addresses the problem of exponential practical stabilization of linear time-invariant systems with disturbances using event-triggered control and bounded communication bit rate. We consider both the case of instantaneous communication with finite precision data at each transmission and the case of non-instantaneous communication with bounded communication rate. Given a prescribed rate of convergence, the proposed event-triggered control implementations opportunistically determine the transmission instants and the finite precision data to be transmitted on each transmission. We show that our design exponentially practically stabilizes the origin while guaranteeing a uniform positive lower bound on the inter-transmission and inter-reception times, ensuring that the number of bits transmitted on each transmission is upper bounded uniformly in time, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted earlier. We also characterize the necessary and sufficient average data rate for exponential practical stabilization. Several simulations illustrate the results.