On Lyapunov inequality characterizations and LMIs based approaches to the L∞(l∞) and L2(l2) semi-global stabilization

Bin Zhou

doi:10.1109/CCDC.2015.7162315

On Lyapunov inequality characterizations and LMIs based approaches to the L_∞(l_∞) and L₂(l₂) semi-global stabilization

Bin Zhou^*

^*Corresponding author for this work

School of Astronautics

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

Abstract

In this paper we provide some new results for L_∞ (l_∞) and L₂ (l₂) semi-global stabilization of (both continuous-time and discrete-time) linear systems with (magnitude and energy) actuator saturation. For the L_∞ (l_∞) and L₂ (l₂) low gain feedback solutions established recently to these two problems, this paper provides new Lyapunov inequalities based characterizations of the L_∞ (l_∞) and L₂ (l₂) low gain feedback. Some new LMIs based solutions to the L_∞ (l_∞) and L₂ (l₂) semi-global stabilization problems are also established.

Original language	English
Title of host publication	Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2357-2362
Number of pages	6
ISBN (Electronic)	9781479970179
DOIs	https://doi.org/10.1109/CCDC.2015.7162315
State	Published - 17 Jul 2015
Event	27th Chinese Control and Decision Conference, CCDC 2015 - Qingdao, China Duration: 23 May 2015 → 25 May 2015

Publication series

Name	Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015

Conference

Conference	27th Chinese Control and Decision Conference, CCDC 2015
Country/Territory	China
City	Qingdao
Period	23/05/15 → 25/05/15

Keywords

L (l) and L (l) low gain feedback
L (l) and L (l) semi-global stabilization
LMIs
Lyapunov inequality
Magnitude and energy saturation

Access to Document

10.1109/CCDC.2015.7162315

Cite this

Zhou, B. (2015). On Lyapunov inequality characterizations and LMIs based approaches to the L_∞(l_∞) and L₂(l₂) semi-global stabilization. In Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015 (pp. 2357-2362). Article 7162315 (Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCDC.2015.7162315

Zhou, Bin. / On Lyapunov inequality characterizations and LMIs based approaches to the L_∞(l_∞) and L₂(l₂) semi-global stabilization. Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 2357-2362 (Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015).

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title = "On Lyapunov inequality characterizations and LMIs based approaches to the L∞(l∞) and L2(l2) semi-global stabilization",

abstract = "In this paper we provide some new results for L∞ (l∞) and L2 (l2) semi-global stabilization of (both continuous-time and discrete-time) linear systems with (magnitude and energy) actuator saturation. For the L∞ (l∞) and L2 (l2) low gain feedback solutions established recently to these two problems, this paper provides new Lyapunov inequalities based characterizations of the L∞ (l∞) and L2 (l2) low gain feedback. Some new LMIs based solutions to the L∞ (l∞) and L2 (l2) semi-global stabilization problems are also established.",

keywords = "L (l) and L (l) low gain feedback, L (l) and L (l) semi-global stabilization, LMIs, Lyapunov inequality, Magnitude and energy saturation",

author = "Bin Zhou",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 27th Chinese Control and Decision Conference, CCDC 2015 ; Conference date: 23-05-2015 Through 25-05-2015",

year = "2015",

month = jul,

day = "17",

doi = "10.1109/CCDC.2015.7162315",

language = "英语",

series = "Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015",

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

pages = "2357--2362",

booktitle = "Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015",

address = "美国",

}

Zhou, B 2015, On Lyapunov inequality characterizations and LMIs based approaches to the L_∞(l_∞) and L₂(l₂) semi-global stabilization. in Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015., 7162315, Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 2357-2362, 27th Chinese Control and Decision Conference, CCDC 2015, Qingdao, China, 23/05/15. https://doi.org/10.1109/CCDC.2015.7162315

On Lyapunov inequality characterizations and LMIs based approaches to the L_∞(l_∞) and L₂(l₂) semi-global stabilization. / Zhou, Bin.
Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2357-2362 7162315 (Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015).

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

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N2 - In this paper we provide some new results for L∞ (l∞) and L2 (l2) semi-global stabilization of (both continuous-time and discrete-time) linear systems with (magnitude and energy) actuator saturation. For the L∞ (l∞) and L2 (l2) low gain feedback solutions established recently to these two problems, this paper provides new Lyapunov inequalities based characterizations of the L∞ (l∞) and L2 (l2) low gain feedback. Some new LMIs based solutions to the L∞ (l∞) and L2 (l2) semi-global stabilization problems are also established.

AB - In this paper we provide some new results for L∞ (l∞) and L2 (l2) semi-global stabilization of (both continuous-time and discrete-time) linear systems with (magnitude and energy) actuator saturation. For the L∞ (l∞) and L2 (l2) low gain feedback solutions established recently to these two problems, this paper provides new Lyapunov inequalities based characterizations of the L∞ (l∞) and L2 (l2) low gain feedback. Some new LMIs based solutions to the L∞ (l∞) and L2 (l2) semi-global stabilization problems are also established.

KW - L (l) and L (l) low gain feedback

KW - L (l) and L (l) semi-global stabilization

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KW - Lyapunov inequality

KW - Magnitude and energy saturation

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Zhou B. On Lyapunov inequality characterizations and LMIs based approaches to the L_∞(l_∞) and L₂(l₂) semi-global stabilization. In Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 2357-2362. 7162315. (Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015). doi: 10.1109/CCDC.2015.7162315