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^*

^*Corresponding author for this work

Research output: Contribution to journal › Conference article in Journal › Research › peer-review

2 Citations (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.

Original language	English
Book series	IFAC-PapersOnLine
Volume	53
Pages (from-to)	7959-7964
Number of pages	6
ISSN	1474-6670
DOIs	https://doi.org/10.1016/j.ifacol.2020.12.2195
Publication status	Published - 2020
Externally published	Yes
Event	21st IFAC World Congress 2020 - Berlin, Germany Duration: 12 Jul 2020 → 17 Jul 2020

Conference

Conference	21st IFAC World Congress 2020
Country/Territory	Germany
City	Berlin
Period	12/07/2020 → 17/07/2020

Bibliographical 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)

Keywords

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

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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",

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

AU - Arceo, Juan Carlos

AU - Lauber, Jimmy

PY - 2020

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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

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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

Abstract

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Bibliographical note

Keywords

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