Copositive conditions for LMI-based controller and observer design

Juan Carlos Arceo; Jimmy Lauber

doi:10.1016/j.ifacol.2020.12.2195

Copositive conditions for LMI-based controller and observer design

Juan Carlos Arceo^*, Jimmy Lauber^*

^*Kontaktforfatter

Publikation: Bidrag til tidsskrift › Konferenceartikel i tidsskrift › Forskning › peer review

2 Citationer (Scopus)

Abstract

In this report we illustrate that nonlinear control and observer design can be described as a Positivstellensatz problem, we consider a quadratic candidate function to stabilize nonlinear systems that have been modeled via the nonlinear sector methodology as an exact convex representation. New shape-independent conditions for satisfying positiveness in double sums are established based on the concept of copositivity. The conditions obtained are compared with previous approaches found in the literature via a numerical example.

Originalsprog	Engelsk
Bogserie	IFAC-PapersOnLine
Vol/bind	53
Sider (fra-til)	7959-7964
Antal sider	6
ISSN	1474-6670
DOI	https://doi.org/10.1016/j.ifacol.2020.12.2195
Status	Udgivet - 2020
Begivenhed	21st IFAC World Congress 2020 - Berlin, Tyskland Varighed: 12 jul. 2020 → 17 jul. 2020

Konference

Konference	21st IFAC World Congress 2020
Land/Område	Tyskland
By	Berlin
Periode	12/07/2020 → 17/07/2020

Bibliografisk note

Publisher Copyright:
Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0)

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10.1016/j.ifacol.2020.12.2195

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@inproceedings{0768d98cb02e44c9a7f7c6ecd2190d0f,

title = "Copositive conditions for LMI-based controller and observer design",

abstract = "In this report we illustrate that nonlinear control and observer design can be described as a Positivstellensatz problem, we consider a quadratic candidate function to stabilize nonlinear systems that have been modeled via the nonlinear sector methodology as an exact convex representation. New shape-independent conditions for satisfying positiveness in double sums are established based on the concept of copositivity. The conditions obtained are compared with previous approaches found in the literature via a numerical example.",

keywords = "Copositive, Exact convex representations, Fuzzy systems, Linear matrix inequalities (LMIs), Nonlinear sector, Relaxed conditions, Takagi-Sugeno",

author = "Arceo, {Juan Carlos} and Jimmy Lauber",

note = "Publisher Copyright: Copyright {\textcopyright} 2020 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0); 21st IFAC World Congress 2020 ; Conference date: 12-07-2020 Through 17-07-2020",

year = "2020",

doi = "10.1016/j.ifacol.2020.12.2195",

language = "English",

volume = "53",

pages = "7959--7964",

journal = "IFAC-PapersOnLine",

issn = "1474-6670",

publisher = "Elsevier",

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TY - GEN

T1 - Copositive conditions for LMI-based controller and observer design

AU - Arceo, Juan Carlos

AU - Lauber, Jimmy

PY - 2020

Y1 - 2020

N2 - In this report we illustrate that nonlinear control and observer design can be described as a Positivstellensatz problem, we consider a quadratic candidate function to stabilize nonlinear systems that have been modeled via the nonlinear sector methodology as an exact convex representation. New shape-independent conditions for satisfying positiveness in double sums are established based on the concept of copositivity. The conditions obtained are compared with previous approaches found in the literature via a numerical example.

AB - In this report we illustrate that nonlinear control and observer design can be described as a Positivstellensatz problem, we consider a quadratic candidate function to stabilize nonlinear systems that have been modeled via the nonlinear sector methodology as an exact convex representation. New shape-independent conditions for satisfying positiveness in double sums are established based on the concept of copositivity. The conditions obtained are compared with previous approaches found in the literature via a numerical example.

KW - Copositive

KW - Exact convex representations

KW - Fuzzy systems

KW - Linear matrix inequalities (LMIs)

KW - Nonlinear sector

KW - Relaxed conditions

KW - Takagi-Sugeno

UR - http://www.scopus.com/inward/record.url?scp=85107638130&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2020.12.2195

DO - 10.1016/j.ifacol.2020.12.2195

M3 - Conference article in Journal

AN - SCOPUS:85107638130

SN - 1474-6670

VL - 53

SP - 7959

EP - 7964

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

T2 - 21st IFAC World Congress 2020

Y2 - 12 July 2020 through 17 July 2020

ER -

Copositive conditions for LMI-based controller and observer design

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