Inter-event Times Analysis for Planar Linear Event-triggered Controlled Systems

Romain Postoyan, Ricardo G. Sanfelice, W.P.M.H. (Maurice) Heemels

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)

Abstract

We analyse the properties of the inter-event times for planar linear time-invariant systems controlled by an event-triggered state-feedback law. The triggering rule is given by the relative threshold strategy and we assume that the tunable triggering parameter is small. Several cases are distinguished depending on the nature of the eigenvalues of the (continuous-time) closed-loop system matrix in absence of sampling. When these eigenvalues are real, it is shown that the inter-event times lie in a neighborhood of a given constant for all positive times or converge to the neighborhood of a given constant as time grows. When the eigenvalues are complex conjugates, the inter-event times oscillate with a varying period for which we give an estimate. Moreover, the values taken by the inter-event times over this varying period are approximately the same for all initial conditions. As a consequence, one can run a single simulation over a given interval of time to infer properties of the inter-event times for all initial conditions and all positive times. Numerical simulations are provided to support the presented theoretical guarantees. These results help to understand the behaviour of the inter-event times, instead of solely relying on numerical simulations, and can be exploited to evaluate the performance of the considered triggering condition in terms of average inter-transmission times.

Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers
Pages1662-1667
Number of pages6
ISBN (Electronic)9781728113982
DOIs
Publication statusPublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: 11 Dec 201913 Dec 2019

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period11/12/1913/12/19

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  • Cite this

    Postoyan, R., Sanfelice, R. G., & Heemels, W. P. M. H. M. (2019). Inter-event Times Analysis for Planar Linear Event-triggered Controlled Systems. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 1662-1667). [9028888] Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC40024.2019.9028888