H controller design for a class of switched linear discrete-time system with polytopic uncertainties

Weiming Xiang, Jian Xiao

Research output: Contribution to journalArticle

Abstract

In this article, a new parameter-dependent stability criterion for switched linear discrete-time systems with polytopic uncertainties is provided to correct an error occurring in previous work, and the parameter-dependent idea is extended to ℓ2 gain analysis problem. Particularly, a less conservative result is proposed by introducing additional slack matrices. Furthermore, the H control problem is investigated. Due to the online calculation characteristic of parameter-dependent controller, a controller structure with less computation cost is of interest. Aside from the controller with the same form as in some existing results involving matrix multiplication and inversion operators, another simple structure of controller formulated by a convex combination of a set of matrices is proposed, which can reduce the online computation cost significantly. A numerical example and results of simulation performed on the model of two-mass-spring mechanical system are provided to illustrate the theoretical findings within this article.

Original languageEnglish (US)
Pages (from-to)1311-1322
Number of pages12
JournalProceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering
Volume226
Issue number10
DOIs
StatePublished - Nov 1 2012
Externally publishedYes

Fingerprint

Controllers
Stability criteria
Costs
Uncertainty

Keywords

  • ℓ gain
  • H control
  • Stability
  • Switched systems
  • Time-varying polytopic uncertainties

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering

Cite this

@article{d8f25be4959a4f99a3e2614c9ea9f254,
title = "H∞ controller design for a class of switched linear discrete-time system with polytopic uncertainties",
abstract = "In this article, a new parameter-dependent stability criterion for switched linear discrete-time systems with polytopic uncertainties is provided to correct an error occurring in previous work, and the parameter-dependent idea is extended to ℓ2 gain analysis problem. Particularly, a less conservative result is proposed by introducing additional slack matrices. Furthermore, the H∞ control problem is investigated. Due to the online calculation characteristic of parameter-dependent controller, a controller structure with less computation cost is of interest. Aside from the controller with the same form as in some existing results involving matrix multiplication and inversion operators, another simple structure of controller formulated by a convex combination of a set of matrices is proposed, which can reduce the online computation cost significantly. A numerical example and results of simulation performed on the model of two-mass-spring mechanical system are provided to illustrate the theoretical findings within this article.",
keywords = "ℓ gain, H control, Stability, Switched systems, Time-varying polytopic uncertainties",
author = "Weiming Xiang and Jian Xiao",
year = "2012",
month = "11",
day = "1",
doi = "10.1177/0959651812458743",
language = "English (US)",
volume = "226",
pages = "1311--1322",
journal = "Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering",
issn = "0959-6518",
publisher = "SAGE Publications Ltd",
number = "10",

}

TY - JOUR

T1 - H∞ controller design for a class of switched linear discrete-time system with polytopic uncertainties

AU - Xiang, Weiming

AU - Xiao, Jian

PY - 2012/11/1

Y1 - 2012/11/1

N2 - In this article, a new parameter-dependent stability criterion for switched linear discrete-time systems with polytopic uncertainties is provided to correct an error occurring in previous work, and the parameter-dependent idea is extended to ℓ2 gain analysis problem. Particularly, a less conservative result is proposed by introducing additional slack matrices. Furthermore, the H∞ control problem is investigated. Due to the online calculation characteristic of parameter-dependent controller, a controller structure with less computation cost is of interest. Aside from the controller with the same form as in some existing results involving matrix multiplication and inversion operators, another simple structure of controller formulated by a convex combination of a set of matrices is proposed, which can reduce the online computation cost significantly. A numerical example and results of simulation performed on the model of two-mass-spring mechanical system are provided to illustrate the theoretical findings within this article.

AB - In this article, a new parameter-dependent stability criterion for switched linear discrete-time systems with polytopic uncertainties is provided to correct an error occurring in previous work, and the parameter-dependent idea is extended to ℓ2 gain analysis problem. Particularly, a less conservative result is proposed by introducing additional slack matrices. Furthermore, the H∞ control problem is investigated. Due to the online calculation characteristic of parameter-dependent controller, a controller structure with less computation cost is of interest. Aside from the controller with the same form as in some existing results involving matrix multiplication and inversion operators, another simple structure of controller formulated by a convex combination of a set of matrices is proposed, which can reduce the online computation cost significantly. A numerical example and results of simulation performed on the model of two-mass-spring mechanical system are provided to illustrate the theoretical findings within this article.

KW - ℓ gain

KW - H control

KW - Stability

KW - Switched systems

KW - Time-varying polytopic uncertainties

UR - http://www.scopus.com/inward/record.url?scp=84877857961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877857961&partnerID=8YFLogxK

U2 - 10.1177/0959651812458743

DO - 10.1177/0959651812458743

M3 - Article

AN - SCOPUS:84877857961

VL - 226

SP - 1311

EP - 1322

JO - Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

JF - Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

SN - 0959-6518

IS - 10

ER -