Backstepping H∞ control for switched nonlinear systems under arbitrary switchings

Ruicheng Ma; Jun Zhao; Georgi M. Dimirovski; Xinquan Zhang

Backstepping H_∞ control for switched nonlinear systems under arbitrary switchings

Ruicheng Ma^*, Jun Zhao, Georgi M. Dimirovski, Xinquan Zhang

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

This paper is concerned with the global H_∞ control problem for a class of switched nonlinear systems in lower triangular form under arbitrary switchings. A common Lyapunov function and a common smooth state feedback controller are constructed by backstepping such that the closed-loop system is globally asymptotically stable under arbitrary switchings without disturbance input and has the prescribed L₂-gain from the disturbance input to the controlled output. The construction of the common virtual controller during the process of backstepping relies on the domination of nonlinearity rather than the cancellation of nonlinearity. A formula is also derived to construct such a common virtual controller. Lastly, an example shows the effectiveness of the proposed method.

Original language	English
Title of host publication	Proceedings of the 2010 American Control Conference, ACC 2010
Pages	1713-1718
Number of pages	6
Publication status	Published - 2010
Event	2010 American Control Conference, ACC 2010 - Baltimore, MD, United States Duration: 30 Jun 2010 → 2 Jul 2010

Publication series

Name	Proceedings of the 2010 American Control Conference, ACC 2010

Conference

Conference	2010 American Control Conference, ACC 2010
Country/Territory	United States
City	Baltimore, MD
Period	30/06/10 → 2/07/10

Cite this

@inproceedings{736686d94af9408b84b69e75c0397bd7,

title = "Backstepping H∞ control for switched nonlinear systems under arbitrary switchings",

abstract = "This paper is concerned with the global H∞ control problem for a class of switched nonlinear systems in lower triangular form under arbitrary switchings. A common Lyapunov function and a common smooth state feedback controller are constructed by backstepping such that the closed-loop system is globally asymptotically stable under arbitrary switchings without disturbance input and has the prescribed L2-gain from the disturbance input to the controlled output. The construction of the common virtual controller during the process of backstepping relies on the domination of nonlinearity rather than the cancellation of nonlinearity. A formula is also derived to construct such a common virtual controller. Lastly, an example shows the effectiveness of the proposed method.",

author = "Ruicheng Ma and Jun Zhao and Dimirovski, {Georgi M.} and Xinquan Zhang",

year = "2010",

language = "English",

isbn = "9781424474264",

series = "Proceedings of the 2010 American Control Conference, ACC 2010",

pages = "1713--1718",

booktitle = "Proceedings of the 2010 American Control Conference, ACC 2010",

note = "2010 American Control Conference, ACC 2010 ; Conference date: 30-06-2010 Through 02-07-2010",

}

Ma, R, Zhao, J, Dimirovski, GM & Zhang, X 2010, Backstepping H_∞ control for switched nonlinear systems under arbitrary switchings. in Proceedings of the 2010 American Control Conference, ACC 2010., 5531501, Proceedings of the 2010 American Control Conference, ACC 2010, pp. 1713-1718, 2010 American Control Conference, ACC 2010, Baltimore, MD, United States, 30/06/10.

Backstepping H_∞ control for switched nonlinear systems under arbitrary switchings. / Ma, Ruicheng; Zhao, Jun; Dimirovski, Georgi M. et al.
Proceedings of the 2010 American Control Conference, ACC 2010. 2010. p. 1713-1718 5531501 (Proceedings of the 2010 American Control Conference, ACC 2010).

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

TY - GEN

T1 - Backstepping H∞ control for switched nonlinear systems under arbitrary switchings

AU - Ma, Ruicheng

AU - Zhao, Jun

AU - Dimirovski, Georgi M.

AU - Zhang, Xinquan

PY - 2010

Y1 - 2010

N2 - This paper is concerned with the global H∞ control problem for a class of switched nonlinear systems in lower triangular form under arbitrary switchings. A common Lyapunov function and a common smooth state feedback controller are constructed by backstepping such that the closed-loop system is globally asymptotically stable under arbitrary switchings without disturbance input and has the prescribed L2-gain from the disturbance input to the controlled output. The construction of the common virtual controller during the process of backstepping relies on the domination of nonlinearity rather than the cancellation of nonlinearity. A formula is also derived to construct such a common virtual controller. Lastly, an example shows the effectiveness of the proposed method.

AB - This paper is concerned with the global H∞ control problem for a class of switched nonlinear systems in lower triangular form under arbitrary switchings. A common Lyapunov function and a common smooth state feedback controller are constructed by backstepping such that the closed-loop system is globally asymptotically stable under arbitrary switchings without disturbance input and has the prescribed L2-gain from the disturbance input to the controlled output. The construction of the common virtual controller during the process of backstepping relies on the domination of nonlinearity rather than the cancellation of nonlinearity. A formula is also derived to construct such a common virtual controller. Lastly, an example shows the effectiveness of the proposed method.

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M3 - Conference contribution

SN - 9781424474264

T3 - Proceedings of the 2010 American Control Conference, ACC 2010

SP - 1713

EP - 1718

BT - Proceedings of the 2010 American Control Conference, ACC 2010

T2 - 2010 American Control Conference, ACC 2010

Y2 - 30 June 2010 through 2 July 2010

ER -

Backstepping H_∞ control for switched nonlinear systems under arbitrary switchings

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