Stability and L2 gain analysis for a class of switched symmetric systems

Guisheng Zhai; Xinkai Chen; Masao Ikeda; Kazunori Yasuda

Stability and L₂ gain analysis for a class of switched symmetric systems

Guisheng Zhai, Xinkai Chen, Masao Ikeda, Kazunori Yasuda

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper, we study stability and L₂ gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric subsystems. We focus our attention mainly on discrete-time systems. When all subsystems are Schur stable, we show that the switched system is exponentially stable under arbitrary switching. Furthermore, we show that when all subsystems are Schur stable and have L₂ gains smaller than a positive scalar γ, the switched system is exponentially stable and has an L₂ gain smaller than the same γ under arbitrary switching. The key idea for both stability and L₂ gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.

Original language	English
Pages (from-to)	4395-4400
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	4
Publication status	Published - 2002
Externally published	Yes
Event	41st IEEE Conference on Decision and Control - Las Vegas, NV, United States Duration: 2002 Dec 10 → 2002 Dec 13

Keywords

Arbitrary switching
Common lyapunov function
Exponential stability
L gain
Linear matrix inequality (LMI)
Switched symmetric system

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Cite this

@article{80685bed53624de0a156fa81654d3c51,

title = "Stability and L2 gain analysis for a class of switched symmetric systems",

abstract = "In this paper, we study stability and L2 gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric subsystems. We focus our attention mainly on discrete-time systems. When all subsystems are Schur stable, we show that the switched system is exponentially stable under arbitrary switching. Furthermore, we show that when all subsystems are Schur stable and have L2 gains smaller than a positive scalar γ, the switched system is exponentially stable and has an L2 gain smaller than the same γ under arbitrary switching. The key idea for both stability and L2 gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.",

keywords = "Arbitrary switching, Common lyapunov function, Exponential stability, L gain, Linear matrix inequality (LMI), Switched symmetric system",

author = "Guisheng Zhai and Xinkai Chen and Masao Ikeda and Kazunori Yasuda",

year = "2002",

language = "English",

volume = "4",

pages = "4395--4400",

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

issn = "0743-1546",

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

note = "41st IEEE Conference on Decision and Control ; Conference date: 10-12-2002 Through 13-12-2002",

}

TY - JOUR

T1 - Stability and L2 gain analysis for a class of switched symmetric systems

AU - Zhai, Guisheng

AU - Chen, Xinkai

AU - Ikeda, Masao

AU - Yasuda, Kazunori

PY - 2002

Y1 - 2002

N2 - In this paper, we study stability and L2 gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric subsystems. We focus our attention mainly on discrete-time systems. When all subsystems are Schur stable, we show that the switched system is exponentially stable under arbitrary switching. Furthermore, we show that when all subsystems are Schur stable and have L2 gains smaller than a positive scalar γ, the switched system is exponentially stable and has an L2 gain smaller than the same γ under arbitrary switching. The key idea for both stability and L2 gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.

AB - In this paper, we study stability and L2 gain properties for a class of switched systems which are composed of a finite number of linear time-invariant symmetric subsystems. We focus our attention mainly on discrete-time systems. When all subsystems are Schur stable, we show that the switched system is exponentially stable under arbitrary switching. Furthermore, we show that when all subsystems are Schur stable and have L2 gains smaller than a positive scalar γ, the switched system is exponentially stable and has an L2 gain smaller than the same γ under arbitrary switching. The key idea for both stability and L2 gain analysis in this paper is to establish a common Lyapunov function for all subsystems in the switched system.

KW - Arbitrary switching

KW - Common lyapunov function

KW - Exponential stability

KW - L gain

KW - Linear matrix inequality (LMI)

KW - Switched symmetric system

UR - http://www.scopus.com/inward/record.url?scp=0038234708&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038234708&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0038234708

SN - 0743-1546

VL - 4

SP - 4395

EP - 4400

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - 41st IEEE Conference on Decision and Control

Y2 - 10 December 2002 through 13 December 2002

ER -

Stability and L₂ gain analysis for a class of switched symmetric systems

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this