Absolute stability and integral control for infinite-dimensional discrete-time systems

J J Coughlan; Hartmut Logemann

doi:10.1016/j.na.2009.03.072

Absolute stability and integral control for infinite-dimensional discrete-time systems

J J Coughlan, Hartmut Logemann

Research output: Contribution to journal › Article › peer-review

8 Citations (SciVal)

223 Downloads (Pure)

Abstract

We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an l(2)-stable linear system and an integrator and the nonlinearity satisfies a sector condition which allows for saturation and deadzone effects. The absolute stability theory is then used to prove tracking and disturbance rejection results for integral control schemes in the presence of input and output nonlinearities. Applications of the input-output theory to state-space systems are also provided.

Original language	English
Pages (from-to)	4769-4789
Number of pages	21
Journal	Nonlinear Analysis: Theory Methods & Applications
Volume	71
Issue number	10
DOIs	https://doi.org/10.1016/j.na.2009.03.072
Publication status	Published - 15 Nov 2009

Keywords

Popov criterion
Integral control
Circle criterion
Infinite-dimensional systems
Discrete-time systems
Nonlinear Volterra difference equations
Absolute stability

Access to Document

10.1016/j.na.2009.03.072

Logemann_NATMA_2009_71_10_4769.pdf
NOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Theory, Methods & Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Theory, Methods & Applications, vol 71 (10), 2009, DOI 10.1016/j.na.2009.03.072
Accepted author manuscript, 4.06 MB

Cite this

@article{32cb5fa009ae4d02bd0b9808b75c4279,

title = "Absolute stability and integral control for infinite-dimensional discrete-time systems",

abstract = "We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an l(2)-stable linear system and an integrator and the nonlinearity satisfies a sector condition which allows for saturation and deadzone effects. The absolute stability theory is then used to prove tracking and disturbance rejection results for integral control schemes in the presence of input and output nonlinearities. Applications of the input-output theory to state-space systems are also provided.",

keywords = "Popov criterion, Integral control, Circle criterion, Infinite-dimensional systems, Discrete-time systems, Nonlinear Volterra difference equations, Absolute stability",

author = "Coughlan, {J J} and Hartmut Logemann",

year = "2009",

month = nov,

day = "15",

doi = "10.1016/j.na.2009.03.072",

language = "English",

volume = "71",

pages = "4769--4789",

journal = "Nonlinear Analysis: Theory Methods & Applications",

issn = "0362-546X",

publisher = "Elsevier",

number = "10",

}

TY - JOUR

T1 - Absolute stability and integral control for infinite-dimensional discrete-time systems

AU - Coughlan, J J

AU - Logemann, Hartmut

PY - 2009/11/15

Y1 - 2009/11/15

N2 - We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an l(2)-stable linear system and an integrator and the nonlinearity satisfies a sector condition which allows for saturation and deadzone effects. The absolute stability theory is then used to prove tracking and disturbance rejection results for integral control schemes in the presence of input and output nonlinearities. Applications of the input-output theory to state-space systems are also provided.

AB - We derive absolute stability results of Popov and circle-criterion types for infinite-dimensional discrete-time systems in an input-output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an l(2)-stable linear system and an integrator and the nonlinearity satisfies a sector condition which allows for saturation and deadzone effects. The absolute stability theory is then used to prove tracking and disturbance rejection results for integral control schemes in the presence of input and output nonlinearities. Applications of the input-output theory to state-space systems are also provided.

KW - Popov criterion

KW - Integral control

KW - Circle criterion

KW - Infinite-dimensional systems

KW - Discrete-time systems

KW - Nonlinear Volterra difference equations

KW - Absolute stability

UR - http://www.scopus.com/inward/record.url?scp=67651121764&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.na.2009.03.072

U2 - 10.1016/j.na.2009.03.072

DO - 10.1016/j.na.2009.03.072

M3 - Article

SN - 0362-546X

VL - 71

SP - 4769

EP - 4789

JO - Nonlinear Analysis: Theory Methods & Applications

JF - Nonlinear Analysis: Theory Methods & Applications

IS - 10

ER -

Absolute stability and integral control for infinite-dimensional discrete-time systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this