Observer-based fault detection for switched systems with all unstable subsystems

Abstract

This paper deals with the fault detection observer design problem for switched system with all modes unstable. First, the error system model is presented. With the consideration of the instability caused by the unobservable condition of $(A_i,C_i)$, a switching signal is obtained via average dwell time method and discretised Lyapunov function. By means of linear matrix inequalities, sufficient conditions pledging exponential stability and $H_{\mathrm{\infty }}$ performance are proposed. Through transferring the observer design problem into $H_{\mathrm{\infty }}$ performance analysis, proper observer gain is obtained via solving these LMIs. In the end, the validity of the proposed Luenberger observer is verified by an example.

Keywords:

• Average dwell time
• discretised Lyapunov function
• weighted $H_{\mathrm{\infty }}$ performance
• Luenberger observer
• unstable subsystems

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [61873057], Natural Science Foundation of Jilin Province [20180520211JH] and Jilin City Science and Technology Bureau [201831727, 201831731].

Notes on contributors

Qingyu Su

Qingyu Su received his B.Sc. degree in electrical automation in 2005, and his M.Sc. degree in control theory and application in 2008, both from Liaoning Technical University, China. He completed his Ph.D. degree in control theory and application in 2013 at Northeastern University, China. Now he is Associate Professor at the School of Automation Engineering, Northeast Electric Power University, China. From October 2015 to October 2016, he was a visiting scholar at the Intelligent Systems and Biomedical Robotics Group (ISR), University of Portsmouth, UK. He has published 21 articles on SCI Journals and 8 papers on international conferences. His research interests include switched systems, nonlinear control systems and power cyber-phyiscal systems.

Zhongxin Fan

Zhongxin Fan received his B.S. degree in Automation from Qufu Normal University in 2017. Now, he is pursuing the M.S. degree in Northeast Electrical Power University. His research interests include switched systems, fault detection and CPSs.

Jian Li

Jian Li received her B.Sc. and M.Sc. degrees in electrical automation and control theory and application from the Liaoning Technical University, China in 2005 and 2008, respectively, and the Ph.D. degree in control theory and application from Northeast University, China in 2013. Currently, she is Associate Professor in the School of Automation Engineering, Northeast Electric Power University, China. From July 2015 to August 2015, she was a visiting scholar at the Nonlinear Dynamics Group, Yeungnam University, South Korea. From October 2016 to October 2017, she was a visiting scholar at National University of Singapore, Singapore. She has published 22 articles on SCI Journals and 9 papers on international conferences. Her research interests include fault detection, robust control and power cyber-physical systems.