Fault detection observer design for periodic piecewise linear systems

Abstract

This article deals with the problem of fault detection observer design for continuous-time periodic piecewise linear systems. Mixed $H_{-}/H_{\mathrm{\infty }}$ performance index is introduced, which results in a trade-off between robustness to unknown input and sensitivity to a fault. Based on a class of Lyapunov functions with time-varying Lyapunov matrices, sufficient conditions are developed to investigate the existence of periodic piecewise fault detection observer with weighted $H_{-}/H_{\mathrm{\infty }}$ performance. A tractable iterative algorithm is proposed to establish the desired periodic piecewise fault detection observer. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

Keywords:

• Fault detection
• $H_{-}/H_{\mathrm{\infty }}$ observer
• iterative algorithm
• periodic piecewise systems

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China (NSFC) [grant number 61973259].

Notes on contributors

Chenchen Fan

Chenchen Fan received the B.E. degree in Automation and the M.E. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2014 and 2016, respectively. She is currently working toward the Ph.D. degree in Mechanical Engineering at The University of Hong Kong, Pokfulam, Hong Kong, as an awardee of the Hong Kong PhD Fellowship Scheme (HKPFS). Her research interests include robust filtering, periodic systems, switched systems, reachable set and robust control.

James Lam

James Lam received a BSc (1st Hons.) degree in Mechanical Engineering from the University of Manchester, and was awarded the Ashbury Scholarship, the A.H. Gibson Prize, and the H. Wright Baker Prize for his academic performance. He obtained the M.Phil. and Ph.D. degrees from the University of Cambridge. He is a Croucher Scholar, Croucher Fellow, and Distinguished Visiting Fellow of the Royal Academy of Engineering. Prior to joining the University of Hong Kong in 1993 where he is now Chair Professor of Control Engineering, he was a lecturer at the City University of Hong Kong and the University of Melbourne. Professor Lam is a Chartered Mathematician, Chartered Scientist, Chartered Engineer, Fellow of Institute of Electrical and Electronic Engineers, Fellow of Institution of Engineering and Technology, Fellow of Institute of Mathematics and Its Applications, Fellow of Institution of Mechanical Engineers, and Fellow of Hong Kong Institution of Engineers. He is Editor-in-Chief of IET Control Theory and Applications and Journal of The Franklin Institute, Subject Editor of Journal of Sound and Vibration, Editor of Asian Journal of Control, Senior Editor of Cogent Engineering, Associate Editor of Automatica, International Journal of Systems Science, Multidimensional Systems and Signal Processing, and Proc. IMechE Part I: Journal of Systems and Control Engineering. He is a member of the Engineering Panel (Joint Research Scheme), Research Grant Council, HKSAR. His research interests include model reduction, robust synthesis, delay, singular systems, stochastic systems, multidimensional systems, positive systems, networked control systems and vibration control. He is a Highly Cited Researcher in Engineering (2014–2019) and Computer Science (2015).

Xiaochen Xie

Xiaochen Xie received the B.E. degree in Automation and the M.E. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2012 and 2014, respectively. She obtained the Ph.D. degree in Control Engineering from The University of Hong Kong in 2018. She was an awardee of the Hong Kong PhD Fellowship Scheme (HKPFS) 2014/15, which supported her doctoral study and academic exchanges. She is currently a Post-doctoral Fellow at Department of Mechanical Engineering, The University of Hong Kong. Her research interests include robust control and filtering, periodic systems, switched systems, intelligent systems and process monitoring.