Event-triggered observer design for linear systems

TL;DR

This paper introduces an event-triggered observer design for linear systems that reduces communication by transmitting output only when necessary, ensuring stability and avoiding Zeno behavior, demonstrated through a battery case study.

Contribution

It proposes a novel event-triggered transmission rule for linear observers, guaranteeing stability and minimum inter-event times, extending existing methods with hybrid system modeling.

Findings

Guarantees global practical asymptotic stability.

Ensures a positive minimum inter-event time.

Validated through a lithium-ion battery case study.

Abstract

We present an event-triggered observer design for linear time-invariant systems, where the measured output is sent to the observer only when a triggering condition is satisfied. We proceed by emulation and we first construct a continuous-time Luenberger observer. We then propose a dynamic rule to trigger transmissions, which only depends on the plant output and an auxiliary scalar state variable. The overall system is modeled as a hybrid system, for which a jump corresponds to an output transmission. We show that the proposed event-triggered observer guarantees global practical asymptotic stability for the estimation error dynamics. Moreover, under mild boundedness conditions on the plant state and its input, we prove that there exists a uniform strictly positive minimum inter-event time between any two consecutive transmissions, guaranteeing that the system does not exhibit Zeno solutions. Finally, the proposed approach is applied to a numerical case study of a lithium-ion battery.