Quadratic Stabilization of Switched Uncertain Linear Systems

Yufang Chang; Bo Fu; Guisheng Zhai

doi:10.1109/CCDC.2018.8407949

Quadratic Stabilization of Switched Uncertain Linear Systems

Yufang Chang, Bo Fu, Guisheng Zhai

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

4 Citations (Scopus)

Abstract

We consider quadratic stabilization for switched systems which are composed of a finite set of linear sub-systems with norm bounded uncertainties. Assuming that no single subsystem has desired quadratic stability, we show that if a convex combination of subsystems is quadratically stable, then we can design a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched system is quadratically stable. When the state information is not available, we extend the discussion to design an output-dependent switching law by constructing a robust Luenberger observer.

Original language	English
Title of host publication	Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4727-4731
Number of pages	5
ISBN (Electronic)	9781538612439
DOIs	https://doi.org/10.1109/CCDC.2018.8407949
Publication status	Published - 2018 Jul 6
Event	30th Chinese Control and Decision Conference, CCDC 2018 - Shenyang, China Duration: 2018 Jun 9 → 2018 Jun 11

Publication series

Name	Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018

Other

Other	30th Chinese Control and Decision Conference, CCDC 2018
Country/Territory	China
City	Shenyang
Period	18/6/9 → 18/6/11

Keywords

LMIs
Switched linear systems (SLS)
convex combination
norm bounded uncertainties
output-dependent switching
quadratic stabilization
state-dependent switching

ASJC Scopus subject areas

Artificial Intelligence
Computer Science Applications
Control and Optimization
Decision Sciences (miscellaneous)

Access to Document

10.1109/CCDC.2018.8407949

Cite this

Chang, Y., Fu, B., & Zhai, G. (2018). Quadratic Stabilization of Switched Uncertain Linear Systems. In Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018 (pp. 4727-4731). (Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCDC.2018.8407949

Quadratic Stabilization of Switched Uncertain Linear Systems. / Chang, Yufang; Fu, Bo; Zhai, Guisheng.

Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 4727-4731 (Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018).

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

Chang, Y, Fu, B & Zhai, G 2018, Quadratic Stabilization of Switched Uncertain Linear Systems. in Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018. Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018, Institute of Electrical and Electronics Engineers Inc., pp. 4727-4731, 30th Chinese Control and Decision Conference, CCDC 2018, Shenyang, China, 18/6/9. https://doi.org/10.1109/CCDC.2018.8407949

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title = "Quadratic Stabilization of Switched Uncertain Linear Systems",

abstract = "We consider quadratic stabilization for switched systems which are composed of a finite set of linear sub-systems with norm bounded uncertainties. Assuming that no single subsystem has desired quadratic stability, we show that if a convex combination of subsystems is quadratically stable, then we can design a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched system is quadratically stable. When the state information is not available, we extend the discussion to design an output-dependent switching law by constructing a robust Luenberger observer.",

keywords = "LMIs, Switched linear systems (SLS), convex combination, norm bounded uncertainties, output-dependent switching, quadratic stabilization, state-dependent switching",

author = "Yufang Chang and Bo Fu and Guisheng Zhai",

note = "Funding Information: This work has been supported in part by the Natural Science Foundation of Hubei Province (2016CFB512) and the Green Industry Leading Program of Hubei University of Technology (CPYF2017003). Publisher Copyright: {\textcopyright} 2018 IEEE.; 30th Chinese Control and Decision Conference, CCDC 2018 ; Conference date: 09-06-2018 Through 11-06-2018",

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AU - Fu, Bo

AU - Zhai, Guisheng

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N2 - We consider quadratic stabilization for switched systems which are composed of a finite set of linear sub-systems with norm bounded uncertainties. Assuming that no single subsystem has desired quadratic stability, we show that if a convex combination of subsystems is quadratically stable, then we can design a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched system is quadratically stable. When the state information is not available, we extend the discussion to design an output-dependent switching law by constructing a robust Luenberger observer.

AB - We consider quadratic stabilization for switched systems which are composed of a finite set of linear sub-systems with norm bounded uncertainties. Assuming that no single subsystem has desired quadratic stability, we show that if a convex combination of subsystems is quadratically stable, then we can design a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched system is quadratically stable. When the state information is not available, we extend the discussion to design an output-dependent switching law by constructing a robust Luenberger observer.

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KW - Switched linear systems (SLS)

KW - convex combination

KW - norm bounded uncertainties

KW - output-dependent switching

KW - quadratic stabilization

KW - state-dependent switching

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ER -

Quadratic Stabilization of Switched Uncertain Linear Systems

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Keywords

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