Stability analysis for switched systems with continuous-time and discrete-time subsystems: A lie algebraic approach

Guisheng Zhai; Derong Liu; Joe Imae; Tomoaki Kobayashi

doi:10.1109/ISCAS.2005.1465304

Stability analysis for switched systems with continuous-time and discrete-time subsystems: A lie algebraic approach

Guisheng Zhai, Derong Liu, Joe Imae, Tomoaki Kobayashi

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

1 Citation (Scopus)

Abstract

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result.

Original language	English
Article number	1465304
Pages (from-to)	3183-3186
Number of pages	4
Journal	Proceedings - IEEE International Symposium on Circuits and Systems
DOIs	https://doi.org/10.1109/ISCAS.2005.1465304
Publication status	Published - 2005 Dec 1
Externally published	Yes
Event	IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005 - Kobe, Japan Duration: 2005 May 23 → 2005 May 26

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/ISCAS.2005.1465304

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title = "Stability analysis for switched systems with continuous-time and discrete-time subsystems: A lie algebraic approach",

abstract = "We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result.",

author = "Guisheng Zhai and Derong Liu and Joe Imae and Tomoaki Kobayashi",

year = "2005",

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doi = "10.1109/ISCAS.2005.1465304",

language = "English",

pages = "3183--3186",

journal = "Proceedings - IEEE International Symposium on Circuits and Systems",

issn = "0271-4310",

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

note = "IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005 ; Conference date: 23-05-2005 Through 26-05-2005",

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TY - JOUR

T1 - Stability analysis for switched systems with continuous-time and discrete-time subsystems

T2 - IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005

AU - Zhai, Guisheng

AU - Liu, Derong

AU - Imae, Joe

AU - Kobayashi, Tomoaki

PY - 2005/12/1

Y1 - 2005/12/1

N2 - We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result.

AB - We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. A numerical example is provided to demonstrate the result.

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DO - 10.1109/ISCAS.2005.1465304

M3 - Conference article

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EP - 3186

JO - Proceedings - IEEE International Symposium on Circuits and Systems

JF - Proceedings - IEEE International Symposium on Circuits and Systems

SN - 0271-4310

M1 - 1465304

Y2 - 23 May 2005 through 26 May 2005

ER -