Stability analysis of non-autonomous switched systems based on time-varying scalar functions

Mengmeng Qiu; Junjie Lu; Weijie Feng; Zhikun She

doi:10.23919/ChiCC.2017.8027718

Stability analysis of non-autonomous switched systems based on time-varying scalar functions

Mengmeng Qiu
, Junjie Lu
, Weijie Feng
, Zhikun She^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

Abstract

In this paper, we investigate asymptotic stability, exponential stability and uniformly exponential stability of non-autonomous switched systems, respectively. Starting with non-autonomous switched linear systems, we firstly provide necessary and sufficient conditions for its asymptotic stability and exponential stability based on the existence of an asymptotically stable function and an exponentially stable function. Successively, a sufficient condition for uniformly exponential stability of a non-autonomous switched linear system is proposed by the existence of an uniformly exponentially stable function. Based on this sufficient condition, we further derive a sufficient condition for local uniformly exponential stability of non-autonomous switched nonlinear systems. In the end, an illustrative example is given to show the applicability of our theoretical results.

Original language	English
Title of host publication	Proceedings of the 36th Chinese Control Conference, CCC 2017
Editors	Tao Liu, Qianchuan Zhao
Publisher	IEEE Computer Society
Pages	2403-2408
Number of pages	6
ISBN (Electronic)	9789881563934
DOIs	https://doi.org/10.23919/ChiCC.2017.8027718
State	Published - 7 Sep 2017
Event	36th Chinese Control Conference, CCC 2017 - Dalian, China Duration: 26 Jul 2017 → 28 Jul 2017

Publication series

Name	Chinese Control Conference, CCC
ISSN (Print)	1934-1768
ISSN (Electronic)	2161-2927

Conference

Conference	36th Chinese Control Conference, CCC 2017
Country/Territory	China
City	Dalian
Period	26/07/17 → 28/07/17

Keywords

Asymptotic stability
Exponential stability
Switched systems
Time-varying scalar functions
Uniformly exponential stability

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10.23919/ChiCC.2017.8027718

Cite this

@inproceedings{ec0b34e40840485fa1ac9a49d626f6a5,

title = "Stability analysis of non-autonomous switched systems based on time-varying scalar functions",

abstract = "In this paper, we investigate asymptotic stability, exponential stability and uniformly exponential stability of non-autonomous switched systems, respectively. Starting with non-autonomous switched linear systems, we firstly provide necessary and sufficient conditions for its asymptotic stability and exponential stability based on the existence of an asymptotically stable function and an exponentially stable function. Successively, a sufficient condition for uniformly exponential stability of a non-autonomous switched linear system is proposed by the existence of an uniformly exponentially stable function. Based on this sufficient condition, we further derive a sufficient condition for local uniformly exponential stability of non-autonomous switched nonlinear systems. In the end, an illustrative example is given to show the applicability of our theoretical results.",

keywords = "Asymptotic stability, Exponential stability, Switched systems, Time-varying scalar functions, Uniformly exponential stability",

author = "Mengmeng Qiu and Junjie Lu and Weijie Feng and Zhikun She",

note = "Publisher Copyright: {\textcopyright} 2017 Technical Committee on Control Theory, CAA.; 36th Chinese Control Conference, CCC 2017 ; Conference date: 26-07-2017 Through 28-07-2017",

year = "2017",

month = sep,

day = "7",

doi = "10.23919/ChiCC.2017.8027718",

language = "英语",

series = "Chinese Control Conference, CCC",

publisher = "IEEE Computer Society",

pages = "2403--2408",

editor = "Tao Liu and Qianchuan Zhao",

booktitle = "Proceedings of the 36th Chinese Control Conference, CCC 2017",

address = "美国",

}

Qiu, M, Lu, J, Feng, W & She, Z 2017, Stability analysis of non-autonomous switched systems based on time-varying scalar functions. in T Liu & Q Zhao (eds), Proceedings of the 36th Chinese Control Conference, CCC 2017., 8027718, Chinese Control Conference, CCC, IEEE Computer Society, pp. 2403-2408, 36th Chinese Control Conference, CCC 2017, Dalian, China, 26/07/17. https://doi.org/10.23919/ChiCC.2017.8027718

Stability analysis of non-autonomous switched systems based on time-varying scalar functions. / Qiu, Mengmeng; Lu, Junjie; Feng, Weijie et al.
Proceedings of the 36th Chinese Control Conference, CCC 2017. ed. / Tao Liu; Qianchuan Zhao. IEEE Computer Society, 2017. p. 2403-2408 8027718 (Chinese Control Conference, CCC).

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

TY - GEN

T1 - Stability analysis of non-autonomous switched systems based on time-varying scalar functions

AU - Qiu, Mengmeng

AU - Lu, Junjie

AU - Feng, Weijie

AU - She, Zhikun

PY - 2017/9/7

Y1 - 2017/9/7

N2 - In this paper, we investigate asymptotic stability, exponential stability and uniformly exponential stability of non-autonomous switched systems, respectively. Starting with non-autonomous switched linear systems, we firstly provide necessary and sufficient conditions for its asymptotic stability and exponential stability based on the existence of an asymptotically stable function and an exponentially stable function. Successively, a sufficient condition for uniformly exponential stability of a non-autonomous switched linear system is proposed by the existence of an uniformly exponentially stable function. Based on this sufficient condition, we further derive a sufficient condition for local uniformly exponential stability of non-autonomous switched nonlinear systems. In the end, an illustrative example is given to show the applicability of our theoretical results.

AB - In this paper, we investigate asymptotic stability, exponential stability and uniformly exponential stability of non-autonomous switched systems, respectively. Starting with non-autonomous switched linear systems, we firstly provide necessary and sufficient conditions for its asymptotic stability and exponential stability based on the existence of an asymptotically stable function and an exponentially stable function. Successively, a sufficient condition for uniformly exponential stability of a non-autonomous switched linear system is proposed by the existence of an uniformly exponentially stable function. Based on this sufficient condition, we further derive a sufficient condition for local uniformly exponential stability of non-autonomous switched nonlinear systems. In the end, an illustrative example is given to show the applicability of our theoretical results.

KW - Asymptotic stability

KW - Exponential stability

KW - Switched systems

KW - Time-varying scalar functions

KW - Uniformly exponential stability

UR - https://www.scopus.com/pages/publications/85032211383

U2 - 10.23919/ChiCC.2017.8027718

DO - 10.23919/ChiCC.2017.8027718

M3 - 会议稿件

AN - SCOPUS:85032211383

T3 - Chinese Control Conference, CCC

SP - 2403

EP - 2408

BT - Proceedings of the 36th Chinese Control Conference, CCC 2017

A2 - Liu, Tao

A2 - Zhao, Qianchuan

PB - IEEE Computer Society

T2 - 36th Chinese Control Conference, CCC 2017

Y2 - 26 July 2017 through 28 July 2017

ER -

Stability analysis of non-autonomous switched systems based on time-varying scalar functions

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