Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance

Lixian Zhang; Songlin Zhuang; Peng Shi; Yanzheng Zhu

doi:10.1109/ACC.2015.7170993

Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance

Lixian Zhang
, Songlin Zhuang
, Peng Shi
, Yanzheng Zhu

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

1 Scopus citations

Abstract

In this paper, the stability problem for a class of discrete-time switched linear systems with bounded additive disturbance is investigated. The disturbance is assumed to be amplitude-bounded and the switching signal is considered to be persistent dwell-time (PDT) switching. The global uniform stability criterion (GUAS) for the nominal switched systems with PDT switching is first established, then a PDT robust positive invariant (RPI) set is determined allowing for the bounded additive disturbance. Based on the PDT RPI set, a concept of generalized robust positive invariant (GRPI) set under PDT switching is further proposed, and it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the PDT GRPI set. A numerical example is provided to verify the theoretical findings.

Original language	English
Title of host publication	ACC 2015 - 2015 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1794-1799
Number of pages	6
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7170993
State	Published - 28 Jul 2015
Externally published	Yes
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: 1 Jul 2015 → 3 Jul 2015

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Conference

Conference	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	1/07/15 → 3/07/15

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10.1109/ACC.2015.7170993

Cite this

Zhang, L., Zhuang, S., Shi, P., & Zhu, Y. (2015). Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance. In ACC 2015 - 2015 American Control Conference (pp. 1794-1799). Article 7170993 (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7170993

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title = "Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance",

abstract = "In this paper, the stability problem for a class of discrete-time switched linear systems with bounded additive disturbance is investigated. The disturbance is assumed to be amplitude-bounded and the switching signal is considered to be persistent dwell-time (PDT) switching. The global uniform stability criterion (GUAS) for the nominal switched systems with PDT switching is first established, then a PDT robust positive invariant (RPI) set is determined allowing for the bounded additive disturbance. Based on the PDT RPI set, a concept of generalized robust positive invariant (GRPI) set under PDT switching is further proposed, and it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the PDT GRPI set. A numerical example is provided to verify the theoretical findings.",

author = "Lixian Zhang and Songlin Zhuang and Peng Shi and Yanzheng Zhu",

note = "Publisher Copyright: {\textcopyright} 2015 American Automatic Control Council.; 2015 American Control Conference, ACC 2015 ; Conference date: 01-07-2015 Through 03-07-2015",

year = "2015",

month = jul,

day = "28",

doi = "10.1109/ACC.2015.7170993",

language = "英语",

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Zhang, L, Zhuang, S, Shi, P & Zhu, Y 2015, Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance. in ACC 2015 - 2015 American Control Conference., 7170993, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 1794-1799, 2015 American Control Conference, ACC 2015, Chicago, United States, 1/07/15. https://doi.org/10.1109/ACC.2015.7170993

Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance. / Zhang, Lixian; Zhuang, Songlin; Shi, Peng et al.
ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1794-1799 7170993 (Proceedings of the American Control Conference; Vol. 2015-July).

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

TY - GEN

T1 - Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance

AU - Zhang, Lixian

AU - Zhuang, Songlin

AU - Shi, Peng

AU - Zhu, Yanzheng

PY - 2015/7/28

Y1 - 2015/7/28

N2 - In this paper, the stability problem for a class of discrete-time switched linear systems with bounded additive disturbance is investigated. The disturbance is assumed to be amplitude-bounded and the switching signal is considered to be persistent dwell-time (PDT) switching. The global uniform stability criterion (GUAS) for the nominal switched systems with PDT switching is first established, then a PDT robust positive invariant (RPI) set is determined allowing for the bounded additive disturbance. Based on the PDT RPI set, a concept of generalized robust positive invariant (GRPI) set under PDT switching is further proposed, and it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the PDT GRPI set. A numerical example is provided to verify the theoretical findings.

AB - In this paper, the stability problem for a class of discrete-time switched linear systems with bounded additive disturbance is investigated. The disturbance is assumed to be amplitude-bounded and the switching signal is considered to be persistent dwell-time (PDT) switching. The global uniform stability criterion (GUAS) for the nominal switched systems with PDT switching is first established, then a PDT robust positive invariant (RPI) set is determined allowing for the bounded additive disturbance. Based on the PDT RPI set, a concept of generalized robust positive invariant (GRPI) set under PDT switching is further proposed, and it is demonstrated that the disturbed system is also asymptotically stable in the sense of converging to the PDT GRPI set. A numerical example is provided to verify the theoretical findings.

UR - https://www.scopus.com/pages/publications/84940923961

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DO - 10.1109/ACC.2015.7170993

M3 - 会议稿件

AN - SCOPUS:84940923961

T3 - Proceedings of the American Control Conference

SP - 1794

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BT - ACC 2015 - 2015 American Control Conference

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2015 American Control Conference, ACC 2015

Y2 - 1 July 2015 through 3 July 2015

ER -

Uniform stability of switched linear systems with persistent dwell-time and bounded additive disturbance

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