Stability of higher-order discrete-time Lur’e systems

E. Sarkans; H. Logemann

doi:10.1016/j.laa.2016.05.012

Stability of higher-order discrete-time Lur’e systems

E. Sarkans
, H. Logemann

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

7 Citations (SciVal)

237 Downloads (Pure)

Abstract

We consider discrete-time Lur’e systems obtained by applying nonlinear feedback to a system of higher-order difference equations (ARMA models). The ARMA model relates the inputs and outputs of the linear system and does not involve any internal or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability, a concept which is very much reminiscent of input-to-state stability.

Original language	English
Pages (from-to)	183-211
Number of pages	30
Journal	Linear Algebra and its Applications
Volume	506
Early online date	26 May 2016
DOIs	https://doi.org/10.1016/j.laa.2016.05.012
Publication status	Published - 1 Oct 2016

Keywords

Absolute stability, ARMA models, circle criterion, complexified Aizerman conjecture, global asymptotic stability, input-to-output stability, input-output systems, Lur’e systems, polynomial matrices, stability in the large

Access to Document

10.1016/j.laa.2016.05.012

io_lure_systems_revised_may_2016Accepted author manuscript, 224 KBLicence: CC BY-NC-ND

http://dx.doi.org/10.1016/j.laa.2016.05.012

Cite this

@article{35cc40cee97b4ad9980efef246ee7eb3,

title = "Stability of higher-order discrete-time Lur{\textquoteright}e systems",

abstract = "We consider discrete-time Lur{\textquoteright}e systems obtained by applying nonlinear feedback to a system of higher-order difference equations (ARMA models). The ARMA model relates the inputs and outputs of the linear system and does not involve any internal or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability, a concept which is very much reminiscent of input-to-state stability.",

keywords = "Absolute stability, ARMA models, circle criterion, complexified Aizerman conjecture, global asymptotic stability, input-to-output stability, input-output systems, Lur{\textquoteright}e systems, polynomial matrices, stability in the large",

author = "E. Sarkans and H. Logemann",

year = "2016",

month = oct,

day = "1",

doi = "10.1016/j.laa.2016.05.012",

language = "English",

volume = "506",

pages = "183--211",

journal = "Linear Algebra and its Applications",

issn = "0024-3795",

publisher = "Elsevier",

}

TY - JOUR

T1 - Stability of higher-order discrete-time Lur’e systems

AU - Sarkans, E.

AU - Logemann, H.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We consider discrete-time Lur’e systems obtained by applying nonlinear feedback to a system of higher-order difference equations (ARMA models). The ARMA model relates the inputs and outputs of the linear system and does not involve any internal or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability, a concept which is very much reminiscent of input-to-state stability.

AB - We consider discrete-time Lur’e systems obtained by applying nonlinear feedback to a system of higher-order difference equations (ARMA models). The ARMA model relates the inputs and outputs of the linear system and does not involve any internal or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability, a concept which is very much reminiscent of input-to-state stability.

KW - Absolute stability, ARMA models, circle criterion, complexified Aizerman conjecture, global asymptotic stability, input-to-output stability, input-output systems, Lur’e systems, polynomial matrices, stability in the large

UR - http://dx.doi.org/10.1016/j.laa.2016.05.012

U2 - 10.1016/j.laa.2016.05.012

DO - 10.1016/j.laa.2016.05.012

M3 - Article

SN - 0024-3795

VL - 506

SP - 183

EP - 211

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Stability of higher-order discrete-time Lur’e systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Hartmut Logemann

Cite this

Stability of higher-order discrete-time Lur’e systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Profiles

Hartmut Logemann

Cite this