Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties

Lixian Zhang; Peng Shi; Michael Basin

doi:10.1109/CDC.2008.4738909

Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties

Lixian Zhang^*
, Peng Shi
, Michael Basin

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

This paper studies the robust stability and stabilization problems for switched linear discrete-time systems. The parameter uncertainties in the system under consideration are time-varying but norm-bounded, and the time delay is assumed to be time-varying and bounded, which covers the constant and mode-dependent constant delays as special cases. First, sufficient conditions are derived to guarantee the stability of the uncertain system. Then, a control law is designed so that the resulting closed-loop system is stable for all admissible uncertainties. A linear matrix inequality (LMIs) approach, together with a cone complementary linearization algorithm, is proposed to solve the above problems. A numerical example is given to show the potential applicability of the obtained theoretic results.

Original language	English
Title of host publication	Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5336-5341
Number of pages	6
ISBN (Print)	9781424431243
DOIs	https://doi.org/10.1109/CDC.2008.4738909
State	Published - 2008
Externally published	Yes
Event	47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: 9 Dec 2008 → 11 Dec 2008

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	47th IEEE Conference on Decision and Control, CDC 2008
Country/Territory	Mexico
City	Cancun
Period	9/12/08 → 11/12/08

Access to Document

10.1109/CDC.2008.4738909

Cite this

Zhang, L., Shi, P., & Basin, M. (2008). Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 5336-5341). Article 4738909 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2008.4738909

@inproceedings{dc65ef064cca4cf6af47352115042779,

title = "Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties",

abstract = "This paper studies the robust stability and stabilization problems for switched linear discrete-time systems. The parameter uncertainties in the system under consideration are time-varying but norm-bounded, and the time delay is assumed to be time-varying and bounded, which covers the constant and mode-dependent constant delays as special cases. First, sufficient conditions are derived to guarantee the stability of the uncertain system. Then, a control law is designed so that the resulting closed-loop system is stable for all admissible uncertainties. A linear matrix inequality (LMIs) approach, together with a cone complementary linearization algorithm, is proposed to solve the above problems. A numerical example is given to show the potential applicability of the obtained theoretic results.",

author = "Lixian Zhang and Peng Shi and Michael Basin",

year = "2008",

doi = "10.1109/CDC.2008.4738909",

language = "英语",

isbn = "9781424431243",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "5336--5341",

booktitle = "Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008",

address = "美国",

note = "47th IEEE Conference on Decision and Control, CDC 2008 ; Conference date: 09-12-2008 Through 11-12-2008",

}

Zhang, L, Shi, P & Basin, M 2008, Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4738909, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5336-5341, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 9/12/08. https://doi.org/10.1109/CDC.2008.4738909

Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties. / Zhang, Lixian; Shi, Peng; Basin, Michael.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc., 2008. p. 5336-5341 4738909 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties

AU - Zhang, Lixian

AU - Shi, Peng

AU - Basin, Michael

PY - 2008

Y1 - 2008

N2 - This paper studies the robust stability and stabilization problems for switched linear discrete-time systems. The parameter uncertainties in the system under consideration are time-varying but norm-bounded, and the time delay is assumed to be time-varying and bounded, which covers the constant and mode-dependent constant delays as special cases. First, sufficient conditions are derived to guarantee the stability of the uncertain system. Then, a control law is designed so that the resulting closed-loop system is stable for all admissible uncertainties. A linear matrix inequality (LMIs) approach, together with a cone complementary linearization algorithm, is proposed to solve the above problems. A numerical example is given to show the potential applicability of the obtained theoretic results.

AB - This paper studies the robust stability and stabilization problems for switched linear discrete-time systems. The parameter uncertainties in the system under consideration are time-varying but norm-bounded, and the time delay is assumed to be time-varying and bounded, which covers the constant and mode-dependent constant delays as special cases. First, sufficient conditions are derived to guarantee the stability of the uncertain system. Then, a control law is designed so that the resulting closed-loop system is stable for all admissible uncertainties. A linear matrix inequality (LMIs) approach, together with a cone complementary linearization algorithm, is proposed to solve the above problems. A numerical example is given to show the potential applicability of the obtained theoretic results.

UR - https://www.scopus.com/pages/publications/62949149053

U2 - 10.1109/CDC.2008.4738909

DO - 10.1109/CDC.2008.4738909

M3 - 会议稿件

AN - SCOPUS:62949149053

SN - 9781424431243

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5336

EP - 5341

BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 47th IEEE Conference on Decision and Control, CDC 2008

Y2 - 9 December 2008 through 11 December 2008

ER -

Zhang L, Shi P, Basin M. Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc. 2008. p. 5336-5341. 4738909. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2008.4738909

Robust stabilization for arbitrarily switched linear systems with time-varying delays and uncertainties

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