The stability analysis of systems with nonlinear feedback expressed by a quadratic program

G Li; WP Heath; B Lennox

doi:10.1109/CDC.2006.376768

The stability analysis of systems with nonlinear feedback expressed by a quadratic program

G Li, WP Heath, B Lennox

Department of Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

7 Citations (Scopus)

409 Downloads (Pure)

Abstract

We consider the stability of the feedback connection of a stable linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program (QP). We establish quadratic constraints from the Karush-Kuhn-Tucker (KKT) conditions that may be used to construct a piecewise quadratic Lyapunov function via the S-procedure. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion. Our approach can be extended to model predictive control (MPC), and gives equivalent results to those in the literature but with a much lower dimension LMI criterion

Translated title of the contribution	The stability analysis of systems with nonlinear feedback expressed by a quadratic program
Original language	English
Title of host publication	the 45th IEEE Conference on Decision and Control, San Diego, California USA
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	4247 - 4252
Number of pages	6
ISBN (Print)	1424401712
DOIs	https://doi.org/10.1109/CDC.2006.376768
Publication status	Published - Dec 2006
Event	45 IEEE Conference on Decision and Control - San Diego, CA, United States Duration: 1 Dec 2006 → …

Conference

Conference	45 IEEE Conference on Decision and Control
Country/Territory	United States
City	San Diego, CA
Period	1/12/06 → …

Bibliographical note

Conference Organiser: IEEE
Rose publication type: Conference contribution

Terms of use: ©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

Keywords

absolute stability
Lur'e systems
LMI
quadratic program

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CDCAccepted author manuscript, 164 KB

http://hdl.handle.net/1983/1609

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title = "The stability analysis of systems with nonlinear feedback expressed by a quadratic program",

abstract = "We consider the stability of the feedback connection of a stable linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program (QP). We establish quadratic constraints from the Karush-Kuhn-Tucker (KKT) conditions that may be used to construct a piecewise quadratic Lyapunov function via the S-procedure. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion. Our approach can be extended to model predictive control (MPC), and gives equivalent results to those in the literature but with a much lower dimension LMI criterion",

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author = "G Li and WP Heath and B Lennox",

note = "Conference Organiser: IEEE Rose publication type: Conference contribution Terms of use: {\textcopyright}2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. ; 45 IEEE Conference on Decision and Control ; Conference date: 01-12-2006",

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language = "English",

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Li, G, Heath, WP & Lennox, B 2006, The stability analysis of systems with nonlinear feedback expressed by a quadratic program. in the 45th IEEE Conference on Decision and Control, San Diego, California USA. Institute of Electrical and Electronics Engineers (IEEE), pp. 4247 - 4252, 45 IEEE Conference on Decision and Control, San Diego, CA, United States, 1/12/06. https://doi.org/10.1109/CDC.2006.376768

The stability analysis of systems with nonlinear feedback expressed by a quadratic program. / Li, G; Heath, WP; Lennox, B.
the 45th IEEE Conference on Decision and Control, San Diego, California USA. Institute of Electrical and Electronics Engineers (IEEE), 2006. p. 4247 - 4252.

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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AU - Li, G

AU - Heath, WP

AU - Lennox, B

N1 - Conference Organiser: IEEE Rose publication type: Conference contribution Terms of use: ©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

PY - 2006/12

Y1 - 2006/12

N2 - We consider the stability of the feedback connection of a stable linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program (QP). We establish quadratic constraints from the Karush-Kuhn-Tucker (KKT) conditions that may be used to construct a piecewise quadratic Lyapunov function via the S-procedure. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion. Our approach can be extended to model predictive control (MPC), and gives equivalent results to those in the literature but with a much lower dimension LMI criterion

AB - We consider the stability of the feedback connection of a stable linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program (QP). We establish quadratic constraints from the Karush-Kuhn-Tucker (KKT) conditions that may be used to construct a piecewise quadratic Lyapunov function via the S-procedure. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion. Our approach can be extended to model predictive control (MPC), and gives equivalent results to those in the literature but with a much lower dimension LMI criterion

KW - absolute stability

KW - Lur'e systems

KW - LMI

KW - quadratic program

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DO - 10.1109/CDC.2006.376768

M3 - Conference Contribution (Conference Proceeding)

SN - 1424401712

SP - 4247

EP - 4252

BT - the 45th IEEE Conference on Decision and Control, San Diego, California USA

PB - Institute of Electrical and Electronics Engineers (IEEE)

T2 - 45 IEEE Conference on Decision and Control

Y2 - 1 December 2006

ER -

The stability analysis of systems with nonlinear feedback expressed by a quadratic program

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Keywords

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