Distributed sampled-data control of Kuramoto-Sivashinsky equation under the point measurements

Wen Kang; Emilia Fridman

doi:10.23919/ECC.2018.8550384

Distributed sampled-data control of Kuramoto-Sivashinsky equation under the point measurements

Wen Kang, Emilia Fridman

School of Electrical Engineering

Tel Aviv University

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

2 Scopus citations

Abstract

We consider sampled-data distributed control of nonlinear PDE system governed by Kuramoto-Sivashinsky equation under point measurements and distributed in space shape functions. It is assumed that the sampling intervals in time and in space are bounded. We derive sufficient conditions ensuring local exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. Moreover, we give a bound on the domain of attraction. As it happened in the case of heat equation, the time-delay approach to sampled-data control and the descriptor method appeared to be efficient tools for the stability analysis of the sampled-data Kuramoto-Sivashinsky equation.

Original language	English
Title of host publication	2018 European Control Conference, ECC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1189-1194
Number of pages	6
ISBN (Electronic)	9783952426982
DOIs	https://doi.org/10.23919/ECC.2018.8550384
State	Published - 27 Nov 2018
Event	16th European Control Conference, ECC 2018 - Limassol, Cyprus Duration: 12 Jun 2018 → 15 Jun 2018

Publication series

Name	2018 European Control Conference, ECC 2018

Conference

Conference	16th European Control Conference, ECC 2018
Country/Territory	Cyprus
City	Limassol
Period	12/06/18 → 15/06/18

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10.23919/ECC.2018.8550384

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title = "Distributed sampled-data control of Kuramoto-Sivashinsky equation under the point measurements",

abstract = "We consider sampled-data distributed control of nonlinear PDE system governed by Kuramoto-Sivashinsky equation under point measurements and distributed in space shape functions. It is assumed that the sampling intervals in time and in space are bounded. We derive sufficient conditions ensuring local exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. Moreover, we give a bound on the domain of attraction. As it happened in the case of heat equation, the time-delay approach to sampled-data control and the descriptor method appeared to be efficient tools for the stability analysis of the sampled-data Kuramoto-Sivashinsky equation.",

author = "Wen Kang and Emilia Fridman",

note = "Publisher Copyright: {\textcopyright} 2018 European Control Association (EUCA).; 16th European Control Conference, ECC 2018 ; Conference date: 12-06-2018 Through 15-06-2018",

year = "2018",

month = nov,

day = "27",

doi = "10.23919/ECC.2018.8550384",

language = "אנגלית",

series = "2018 European Control Conference, ECC 2018",

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

pages = "1189--1194",

booktitle = "2018 European Control Conference, ECC 2018",

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Kang, W & Fridman, E 2018, Distributed sampled-data control of Kuramoto-Sivashinsky equation under the point measurements. in 2018 European Control Conference, ECC 2018., 8550384, 2018 European Control Conference, ECC 2018, Institute of Electrical and Electronics Engineers Inc., pp. 1189-1194, 16th European Control Conference, ECC 2018, Limassol, Cyprus, 12/06/18. https://doi.org/10.23919/ECC.2018.8550384

Distributed sampled-data control of Kuramoto-Sivashinsky equation under the point measurements. / Kang, Wen; Fridman, Emilia.
2018 European Control Conference, ECC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1189-1194 8550384 (2018 European Control Conference, ECC 2018).

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

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N2 - We consider sampled-data distributed control of nonlinear PDE system governed by Kuramoto-Sivashinsky equation under point measurements and distributed in space shape functions. It is assumed that the sampling intervals in time and in space are bounded. We derive sufficient conditions ensuring local exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. Moreover, we give a bound on the domain of attraction. As it happened in the case of heat equation, the time-delay approach to sampled-data control and the descriptor method appeared to be efficient tools for the stability analysis of the sampled-data Kuramoto-Sivashinsky equation.

AB - We consider sampled-data distributed control of nonlinear PDE system governed by Kuramoto-Sivashinsky equation under point measurements and distributed in space shape functions. It is assumed that the sampling intervals in time and in space are bounded. We derive sufficient conditions ensuring local exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. Moreover, we give a bound on the domain of attraction. As it happened in the case of heat equation, the time-delay approach to sampled-data control and the descriptor method appeared to be efficient tools for the stability analysis of the sampled-data Kuramoto-Sivashinsky equation.

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Distributed sampled-data control of Kuramoto-Sivashinsky equation under the point measurements

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