Analysis and synthesis of uncertain switched discrete-time systems

Magdi S. Mahmoud, Mohamed Nounou, Hazem Nounou

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

The problems of L2-gain analysis and control synthesis for a class of linear discrete-time switched systems with convex-bounded parameter uncertainties in all system matrices are investigated. The main thrust is based on the constructive use of an appropriate switched Lyapunov functional. The L2-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an L2 gain smaller than a prescribed constant level. The control synthesis is to design switched feedback schemes, whether based on state-, output measurements or by using dynamic output feedback, to guarantee that the corresponding closed-loop system enjoys the uniform quadratic stability with an L2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over linear matrix inequalities and tested on representative examples.

Original languageEnglish
Pages (from-to)245-257
Number of pages13
JournalIMA Journal of Mathematical Control and Information
Volume24
Issue number2
DOIs
Publication statusPublished - Jun 2007

Fingerprint

Switched Systems
Discrete-time Systems
Synthesis
Feedback
Convex optimization
Linear matrix inequalities
Closed loop systems
Quadratic Stability
Polytopic Uncertainty
Switched Linear Systems
Uniform Stability
Dynamic Output Feedback
Lyapunov Functional
Parameter Uncertainty
Convex Optimization
Closed-loop System
Matrix Inequality
Linear Inequalities
Uncertainty
Output

Keywords

  • Lmis
  • Polytopic uncertainty
  • Switched output feedback
  • Switched state feedback
  • Switched systems
  • Uniform quadratic stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Systems Engineering
  • Control and Optimization

Cite this

Analysis and synthesis of uncertain switched discrete-time systems. / Mahmoud, Magdi S.; Nounou, Mohamed; Nounou, Hazem.

In: IMA Journal of Mathematical Control and Information, Vol. 24, No. 2, 06.2007, p. 245-257.

Research output: Contribution to journalArticle

@article{e4168e351373447ab98beab91c240e1c,
title = "Analysis and synthesis of uncertain switched discrete-time systems",
abstract = "The problems of L2-gain analysis and control synthesis for a class of linear discrete-time switched systems with convex-bounded parameter uncertainties in all system matrices are investigated. The main thrust is based on the constructive use of an appropriate switched Lyapunov functional. The L2-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an L2 gain smaller than a prescribed constant level. The control synthesis is to design switched feedback schemes, whether based on state-, output measurements or by using dynamic output feedback, to guarantee that the corresponding closed-loop system enjoys the uniform quadratic stability with an L2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over linear matrix inequalities and tested on representative examples.",
keywords = "Lmis, Polytopic uncertainty, Switched output feedback, Switched state feedback, Switched systems, Uniform quadratic stability",
author = "Mahmoud, {Magdi S.} and Mohamed Nounou and Hazem Nounou",
year = "2007",
month = "6",
doi = "10.1093/imamci/dnl021",
language = "English",
volume = "24",
pages = "245--257",
journal = "IMA Journal of Mathematical Control and Information",
issn = "0265-0754",
publisher = "Oxford University Press",
number = "2",

}

TY - JOUR

T1 - Analysis and synthesis of uncertain switched discrete-time systems

AU - Mahmoud, Magdi S.

AU - Nounou, Mohamed

AU - Nounou, Hazem

PY - 2007/6

Y1 - 2007/6

N2 - The problems of L2-gain analysis and control synthesis for a class of linear discrete-time switched systems with convex-bounded parameter uncertainties in all system matrices are investigated. The main thrust is based on the constructive use of an appropriate switched Lyapunov functional. The L2-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an L2 gain smaller than a prescribed constant level. The control synthesis is to design switched feedback schemes, whether based on state-, output measurements or by using dynamic output feedback, to guarantee that the corresponding closed-loop system enjoys the uniform quadratic stability with an L2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over linear matrix inequalities and tested on representative examples.

AB - The problems of L2-gain analysis and control synthesis for a class of linear discrete-time switched systems with convex-bounded parameter uncertainties in all system matrices are investigated. The main thrust is based on the constructive use of an appropriate switched Lyapunov functional. The L2-gain analysis is to characterize conditions under which the linear switched system with polytopic uncertainties is uniformly quadratically stable with an L2 gain smaller than a prescribed constant level. The control synthesis is to design switched feedback schemes, whether based on state-, output measurements or by using dynamic output feedback, to guarantee that the corresponding closed-loop system enjoys the uniform quadratic stability with an L2 gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over linear matrix inequalities and tested on representative examples.

KW - Lmis

KW - Polytopic uncertainty

KW - Switched output feedback

KW - Switched state feedback

KW - Switched systems

KW - Uniform quadratic stability

UR - http://www.scopus.com/inward/record.url?scp=57349173026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57349173026&partnerID=8YFLogxK

U2 - 10.1093/imamci/dnl021

DO - 10.1093/imamci/dnl021

M3 - Article

VL - 24

SP - 245

EP - 257

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

SN - 0265-0754

IS - 2

ER -