On equivalence of two stability criteria for continuous-time switched systems with dwell time constraint

Weiming Xiang

doi:10.1016/j.automatica.2015.01.033

On equivalence of two stability criteria for continuous-time switched systems with dwell time constraint

Weiming Xiang

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

85 Scopus citations

Abstract

In this note, a study on the equivalence of two stability criteria for continuous-time switched linear systems with dwell time constraint is presented. It is demonstrated that, for any dwell time satisfying the conditions in stability criterion proposed in Geromel and Colaneri (2006), the conditions in stability criterion of Allerhand and Shaked (2011) also hold as long as the number of decision variables and related LMIs is sufficiently large, which implies the two stability criteria are intrinsically equivalent. The equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and LMIs. A numerical example is proposed to illustrate the theoretical results, and an extension to uncertain case is briefly presented.

Original language	English (US)
Pages (from-to)	36-40
Number of pages	5
Journal	Automatica
Volume	54
DOIs	https://doi.org/10.1016/j.automatica.2015.01.033
State	Published - Apr 1 2015
Externally published	Yes

Keywords

Continuous-time switched linear system
Dwell time
Stability

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/j.automatica.2015.01.033

Cite this

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title = "On equivalence of two stability criteria for continuous-time switched systems with dwell time constraint",

abstract = "In this note, a study on the equivalence of two stability criteria for continuous-time switched linear systems with dwell time constraint is presented. It is demonstrated that, for any dwell time satisfying the conditions in stability criterion proposed in Geromel and Colaneri (2006), the conditions in stability criterion of Allerhand and Shaked (2011) also hold as long as the number of decision variables and related LMIs is sufficiently large, which implies the two stability criteria are intrinsically equivalent. The equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and LMIs. A numerical example is proposed to illustrate the theoretical results, and an extension to uncertain case is briefly presented.",

keywords = "Continuous-time switched linear system, Dwell time, Stability",

author = "Weiming Xiang",

note = "Funding Information: This work is supported by the National Natural Science Foundation of China ( 51177137 , 61134001 ). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor A. Pedro Aguiar under the direction of Editor Andr{\'e} L. Tits. Publisher Copyright: {\textcopyright} 2015 Elsevier Ltd. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

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doi = "10.1016/j.automatica.2015.01.033",

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AU - Xiang, Weiming

N1 - Funding Information: This work is supported by the National Natural Science Foundation of China ( 51177137 , 61134001 ). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor A. Pedro Aguiar under the direction of Editor André L. Tits. Publisher Copyright: © 2015 Elsevier Ltd. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015/4/1

Y1 - 2015/4/1

N2 - In this note, a study on the equivalence of two stability criteria for continuous-time switched linear systems with dwell time constraint is presented. It is demonstrated that, for any dwell time satisfying the conditions in stability criterion proposed in Geromel and Colaneri (2006), the conditions in stability criterion of Allerhand and Shaked (2011) also hold as long as the number of decision variables and related LMIs is sufficiently large, which implies the two stability criteria are intrinsically equivalent. The equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and LMIs. A numerical example is proposed to illustrate the theoretical results, and an extension to uncertain case is briefly presented.

AB - In this note, a study on the equivalence of two stability criteria for continuous-time switched linear systems with dwell time constraint is presented. It is demonstrated that, for any dwell time satisfying the conditions in stability criterion proposed in Geromel and Colaneri (2006), the conditions in stability criterion of Allerhand and Shaked (2011) also hold as long as the number of decision variables and related LMIs is sufficiently large, which implies the two stability criteria are intrinsically equivalent. The equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and LMIs. A numerical example is proposed to illustrate the theoretical results, and an extension to uncertain case is briefly presented.

KW - Continuous-time switched linear system

KW - Dwell time

KW - Stability

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JO - Automatica

JF - Automatica

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On equivalence of two stability criteria for continuous-time switched systems with dwell time constraint

Abstract

Keywords

ASJC Scopus subject areas

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