Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable

Shaoxia Feng; Juan Wang; Jun Zhao

doi:10.1109/JAS.2017.7510718

Volume 6 Issue 1

Jan. 2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2019 > 6(1): 167-176

Shaoxia Feng, Juan Wang and Jun Zhao, "Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 167-176, Jan. 2019. doi: 10.1109/JAS.2017.7510718

Citation:

Shaoxia Feng, Juan Wang and Jun Zhao, "Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable," IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 167-176, Jan. 2019. doi: 10.1109/JAS.2017.7510718

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Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable

doi: 10.1109/JAS.2017.7510718

Shaoxia Feng^{1, 2
,},
Juan Wang^{3
,
,},
Jun Zhao^4
,

1.
Shanxi Institute of Mechanical and Electrical Engineering, Changzhi 046011
2.
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
3.
Faculty of Information and Control Engineering, Shenyang Jianzhu University, Shenyang 110168, China
4.
State Key Laboratory of Synthetical Automation for Process Industries (Northeastern University), and also with the College of Information Science and Engineering, Northeastern University, Shenyang 110819, China

Funds:

National Natural Science Foundation of China 61703288

National Natural Science Foundation of China 61603079

National Natural Science Foundation of China 61873174

More Information

Author Bio:
Shaoxia Feng received the B.S. degree in mathematics and applied mathematics from China University of Mining and Technology in 2014, and M.S. degree in control theory and control engineering from Northeastern University in 2017. Her research interests include switched systems, switched positive system, and robust control. (e-mail: fengshaoxianeu@163.com)

Juan Wang is a Lecturer for the Faculty of Information and Control Engineering of Shenyang Jianzhu University, China. She received the B.S. degree in mathematics and applied mathematics from Bohai University, China, in 2007, and the M.S. degree in operational research and cybernetics from Northeastern University, China, in 2009. She received the Ph.D. degree in control theory and applications in 2016 at Northeastern University, China. Her research interests include switched systems, positive system, and actuator saturation

Jun Zhao received the B.S. and M.S. degrees in mathematics in 1982 and 1984, respectively, both from Liaoning University, China. He received the Ph.D. degree in control theory and applications in 1991 at Northeastern University, China. From 1992 to 1993 he was a Postdoctoral Fellow at the same university. Since 1994, as a Professor, he has been with the College of Information Science and Engineering, Northeastern University, China. From 1998 to 1999, he was a Senior Visiting Scholar at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, USA. From November 2003 to May 2005, he was a Research Fellow in the Department of Electronic Engineering, City University of Hong Kong. During 2007-2010, he was a Fellow at the School of Engineering, Australian National University. His research interests include switched systems, nonlinear systems and network synchronization. (e-mail: zhaojun@mail.neu.edu.cn)
Corresponding author: Juan Wang, e-mail: wangjuanneu@163.com
Received Date: 2016-09-23
Revised Date: 2017-05-27
Accepted Date: 2017-07-06

Abstract

Abstract

This paper is concerned with the stability and robust stability of switched positive linear systems (SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.
- Discretized co-positive Lyapunov functions,
- mode-dependent dwell time,
- robust stability,
- switched positive linear systems (SPLSs),
- unstable subsystem

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References(30)

References

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Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable

doi: 10.1109/JAS.2017.7510718

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