Sampled-data observer for 2D Navier-Stokes equation

Wen Kang; Emilia Fridman; Sergiy Zhuk

doi:10.1109/CDC40024.2019.9029275

Sampled-data observer for 2D Navier-Stokes equation

Wen Kang, Emilia Fridman, Sergiy Zhuk

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

Abstract

We consider sampled-data observer for PDE system governed by the Navier-Stokes equation on the rectangular domain. The system is exponentially stable. We aim to design an observer that exponentially converges to solution with a higher decay rate. We suggested to divide the rectangular domain into N square subdomains, where sensors provide spatially averaged discrete-time state measurements. We derive sufficient conditions ensuring regional exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. The efficiency of the results is demonstrated by a numerical example.

Original language	English
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1201-1206
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9029275
Publication status	Published - Dec 2019
Externally published	Yes
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: 11 Dec 2019 → 13 Dec 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	11/12/19 → 13/12/19

Access to Document

10.1109/CDC40024.2019.9029275

Cite this

Kang, W., Fridman, E., & Zhuk, S. (2019). Sampled-data observer for 2D Navier-Stokes equation. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 1201-1206). Article 9029275 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029275

@inproceedings{b8d63e8eeba14baab4cd0e334724d4c1,

title = "Sampled-data observer for 2D Navier-Stokes equation",

abstract = "We consider sampled-data observer for PDE system governed by the Navier-Stokes equation on the rectangular domain. The system is exponentially stable. We aim to design an observer that exponentially converges to solution with a higher decay rate. We suggested to divide the rectangular domain into N square subdomains, where sensors provide spatially averaged discrete-time state measurements. We derive sufficient conditions ensuring regional exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. The efficiency of the results is demonstrated by a numerical example.",

author = "Wen Kang and Emilia Fridman and Sergiy Zhuk",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 58th IEEE Conference on Decision and Control, CDC 2019 ; Conference date: 11-12-2019 Through 13-12-2019",

year = "2019",

month = dec,

doi = "10.1109/CDC40024.2019.9029275",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1201--1206",

booktitle = "2019 IEEE 58th Conference on Decision and Control, CDC 2019",

address = "United States",

}

Kang, W, Fridman, E & Zhuk, S 2019, Sampled-data observer for 2D Navier-Stokes equation. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9029275, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, Institute of Electrical and Electronics Engineers Inc., pp. 1201-1206, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 11/12/19. https://doi.org/10.1109/CDC40024.2019.9029275

Sampled-data observer for 2D Navier-Stokes equation. / Kang, Wen; Fridman, Emilia; Zhuk, Sergiy.
2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1201-1206 9029275 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Sampled-data observer for 2D Navier-Stokes equation

AU - Kang, Wen

AU - Fridman, Emilia

AU - Zhuk, Sergiy

PY - 2019/12

Y1 - 2019/12

N2 - We consider sampled-data observer for PDE system governed by the Navier-Stokes equation on the rectangular domain. The system is exponentially stable. We aim to design an observer that exponentially converges to solution with a higher decay rate. We suggested to divide the rectangular domain into N square subdomains, where sensors provide spatially averaged discrete-time state measurements. We derive sufficient conditions ensuring regional exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. The efficiency of the results is demonstrated by a numerical example.

AB - We consider sampled-data observer for PDE system governed by the Navier-Stokes equation on the rectangular domain. The system is exponentially stable. We aim to design an observer that exponentially converges to solution with a higher decay rate. We suggested to divide the rectangular domain into N square subdomains, where sensors provide spatially averaged discrete-time state measurements. We derive sufficient conditions ensuring regional exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. The efficiency of the results is demonstrated by a numerical example.

UR - http://www.scopus.com/inward/record.url?scp=85082484403&partnerID=8YFLogxK

U2 - 10.1109/CDC40024.2019.9029275

DO - 10.1109/CDC40024.2019.9029275

M3 - Conference contribution

AN - SCOPUS:85082484403

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1201

EP - 1206

BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 58th IEEE Conference on Decision and Control, CDC 2019

Y2 - 11 December 2019 through 13 December 2019

ER -

Sampled-data observer for 2D Navier-Stokes equation

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this