Stability of a class of linear switching systems with time delay

Sehjeong Kim; Sue Ann Campbell; Xinzhi Liu

doi:10.1109/TCSI.2005.856666

Stability of a class of linear switching systems with time delay

Sehjeong Kim, Sue Ann Campbell, Xinzhi Liu

Research output: Contribution to journal › Article › peer-review

266 Citations (Scopus)

Abstract

We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay.

Original language	English
Pages (from-to)	384-393
Number of pages	10
Journal	IEEE Transactions on Circuits and Systems I: Regular Papers
Volume	53
Issue number	2
DOIs	https://doi.org/10.1109/TCSI.2005.856666
Publication status	Published - 2006
Externally published	Yes

Keywords

Delay differential equations (DDEs)
Lyapunov functional
Switching systems

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TCSI.2005.856666

Cite this

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title = "Stability of a class of linear switching systems with time delay",

abstract = "We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay.",

keywords = "Delay differential equations (DDEs), Lyapunov functional, Switching systems",

author = "Sehjeong Kim and Campbell, {Sue Ann} and Xinzhi Liu",

note = "Funding Information: Manuscript received September 17, 2004; revised March 30, 2005. This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. This paper was recommended by Associate Editor C. Hadjicostis. The authors are with the Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: sacampbell@uwaterloo.ca). Digital Object Identifier 10.1109/TCSI.2005.856666",

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AU - Kim, Sehjeong

AU - Campbell, Sue Ann

AU - Liu, Xinzhi

N1 - Funding Information: Manuscript received September 17, 2004; revised March 30, 2005. This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. This paper was recommended by Associate Editor C. Hadjicostis. The authors are with the Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: sacampbell@uwaterloo.ca). Digital Object Identifier 10.1109/TCSI.2005.856666

PY - 2006

Y1 - 2006

N2 - We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay.

AB - We consider a switching system composed of a finite number of linear delay differential equations (DDEs). It has been shown that the stability of a switching system composed of a finite number of linear ordinary differential equations (ODEs) may be achieved by using a common Lyapunov function method switching rule. We modify this switching rule for ODE systems to a common Lyapunov functional method switching rule for DDE systems and show that it stabilizes our model. Our result uses a Riccati-type Lyapunov functional under a condition on the time delay.

KW - Delay differential equations (DDEs)

KW - Lyapunov functional

KW - Switching systems

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Stability of a class of linear switching systems with time delay

Abstract

Keywords

ASJC Scopus subject areas

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