Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign

D. W. Kim, Jin Bae Park, Y. H. Joo

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique.

Original languageEnglish
Pages (from-to)1070-1080
Number of pages11
JournalIET Control Theory and Applications
Volume3
Issue number8
DOIs
Publication statusPublished - 2009 Aug 21

Fingerprint

Sampled data control systems
Digital Redesign
Sampled-data Control
Sampled-data Systems
Nonlinear control systems
Robust Stabilization
Nonlinear Perturbations
Stabilization
Control System
Continuous Time
Controllers
Nonlinear Control Systems
Perturbed System
Linear matrix inequalities
Trajectories
Perturbation
Controller
Matrix Inequality
Convergence Rate
Linear Time

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Control and Optimization
  • Electrical and Electronic Engineering

Cite this

@article{c71fbeaec0e943f9bf4f9872a92d8416,
title = "Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign",
abstract = "This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique.",
author = "Kim, {D. W.} and Park, {Jin Bae} and Joo, {Y. H.}",
year = "2009",
month = "8",
day = "21",
doi = "10.1049/iet-cta.2008.0133",
language = "English",
volume = "3",
pages = "1070--1080",
journal = "IET Control Theory and Applications",
issn = "1751-8644",
publisher = "Institution of Engineering and Technology",
number = "8",

}

Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign. / Kim, D. W.; Park, Jin Bae; Joo, Y. H.

In: IET Control Theory and Applications, Vol. 3, No. 8, 21.08.2009, p. 1070-1080.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign

AU - Kim, D. W.

AU - Park, Jin Bae

AU - Joo, Y. H.

PY - 2009/8/21

Y1 - 2009/8/21

N2 - This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique.

AB - This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique.

UR - http://www.scopus.com/inward/record.url?scp=68849130658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68849130658&partnerID=8YFLogxK

U2 - 10.1049/iet-cta.2008.0133

DO - 10.1049/iet-cta.2008.0133

M3 - Article

VL - 3

SP - 1070

EP - 1080

JO - IET Control Theory and Applications

JF - IET Control Theory and Applications

SN - 1751-8644

IS - 8

ER -