Nyquist stability criteria for control systems with stochastic delays

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

Abstract

We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

LanguageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages270-275
Number of pages6
ISBN (Electronic)978-1-5386-1395-5
ISBN (Print)978-1-5386-1396-2
DOIs
StatePublished - 18 Jan 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: 17 Dec 201819 Dec 2018
Conference number: 57

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
Abbreviated titleCDC 2018
CountryUnited States
CityMiami
Period17/12/1819/12/18

Fingerprint

Stability criteria
Stability Criteria
Linear systems
Control System
Control systems
Moment
Random variables
Probability distributions
Linear Systems
Almost Sure Stability
Positive Systems
Mean-square Stability
Linear Control
Time-varying Delay
Identically distributed
Margin
Probability Distribution
Random variable
First-order
Numerical Examples

Cite this

Antunes, D. J. (2019). Nyquist stability criteria for control systems with stochastic delays. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 270-275). [8619247] Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.1109/CDC.2018.8619247
Antunes, Duarte J./ Nyquist stability criteria for control systems with stochastic delays. 2018 IEEE Conference on Decision and Control, CDC 2018. Piscataway : Institute of Electrical and Electronics Engineers, 2019. pp. 270-275
@inproceedings{922b457daa384a379086861ac57f2381,
title = "Nyquist stability criteria for control systems with stochastic delays",
abstract = "We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.",
author = "Antunes, {Duarte J.}",
year = "2019",
month = "1",
day = "18",
doi = "10.1109/CDC.2018.8619247",
language = "English",
isbn = "978-1-5386-1396-2",
pages = "270--275",
booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",
publisher = "Institute of Electrical and Electronics Engineers",
address = "United States",

}

Antunes, DJ 2019, Nyquist stability criteria for control systems with stochastic delays. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619247, Institute of Electrical and Electronics Engineers, Piscataway, pp. 270-275, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. DOI: 10.1109/CDC.2018.8619247

Nyquist stability criteria for control systems with stochastic delays. / Antunes, Duarte J.

2018 IEEE Conference on Decision and Control, CDC 2018. Piscataway : Institute of Electrical and Electronics Engineers, 2019. p. 270-275 8619247.

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

TY - GEN

T1 - Nyquist stability criteria for control systems with stochastic delays

AU - Antunes,Duarte J.

PY - 2019/1/18

Y1 - 2019/1/18

N2 - We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

AB - We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

UR - http://www.scopus.com/inward/record.url?scp=85062175002&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619247

DO - 10.1109/CDC.2018.8619247

M3 - Conference contribution

SN - 978-1-5386-1396-2

SP - 270

EP - 275

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -

Antunes DJ. Nyquist stability criteria for control systems with stochastic delays. In 2018 IEEE Conference on Decision and Control, CDC 2018. Piscataway: Institute of Electrical and Electronics Engineers. 2019. p. 270-275. 8619247. Available from, DOI: 10.1109/CDC.2018.8619247