Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

ABSTRACT

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman–Yakubovic–Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H₋ and H_∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

KEYWORDS:

• Multiple time-varying delay
• fault detection filter
• finite frequency
• continuous-time singular switched linear systems
• linear matrix inequalities

Acknowledgements

The authors are grateful to the editors and the anonymous reviewers for their helpful comments and suggestion on this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Funds of National Science of China [grant number 61473068]; the Nature Science of Foundation of Liaoning Province [grant number 2014020019]; the Nature Science of Foundation of Shenyang [grant number F14-231-1-02]; the General Project of Liaoning Province Department of Education [grant number L20150182]; and the Fundamental Research Funds for the Central Universities [grant number N140402002].

Notes on contributors

Ding Zhai

Ding Zhai received his BS, MS, and PhD degrees from Northeastern University, China, in 1992, 1999, and 2004, respectively. He visited the Nanyang Technological University in 2004 as a research fellow. He is now an associate professor at Northeastern University. His research interests focus on fault detection.

Anyang Lu

Anyang Lu received his BS degree in mathematics from Northeastern University, China, in 2014. He is now pursuing his MS degree in systems theory at Northeastern University, China. His current research interests focus on fault detection, switched systems, andT-S fuzzy systems.

Jinghao Li

Jinghao Li received his BSc degree in Mathematics from Northeastern University, China, in 2011, and MSc degree in systems theory from Northeastern University, China, in 2013. He is now pursuing his PhD degree in control theory and control engineering at Northeastern University, China. His current research interests focus on sliding mode control, descriptor system, and Markovian jump system.

Qingling Zhang

Qingling Zhang received his BS and MS degrees from the Mathematics Department and PhD degree from the Automatic Control Department of Northeastern University, Shenyang, China, in 1982, 1986, and 1995, respectively. Dr Zhang is now a professor at Northeastern University. His research interests include descriptor system.