Finite frequency fault estimation observer design for T-S Fuzzy discrete-time descriptor systems

Abstract

This paper deals with the problem of $H_{\mathrm{\infty }}$ fault estimation observer design for T-S fuzzy nonlinear discrete-time descriptor systems in the finite frequency domain. First, a novel fault estimation observer for the augmented descriptor system is given. Based on Parseval's theorem and Lyapunov theory, the performance in the finite frequency domain is derived via time-domain method. Then, new sufficient conditions of admissibility and robust performance index for the dynamic error system are obtained as bilinear matrix inequalities. Meanwhile, an iterative linear matrix inequality algorithm is given to obtain the optimal solution. Finally, an example is given to demonstrate the effectiveness of our method.

Keywords:

• Descriptor systems
• discrete-time T-S fuzzy systems
• GKYP lemma

Disclosure statement

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

Additional information

Funding

This paper is partly supported by the the National Science Foundation of China [grant number 61625305], the Natural Science Foundation of Hubei Province [grant number 2018CFC816], WUST National Defence Pre-research foundation [grant number GF201813], the Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China (No.ICT20082).

Notes on contributors

Yimin Liu

Yimin Liu received the M.S. degree in Pattern Recognition and Intelligent System from Beijing Institute of Technology, Beijing, China, in 2000. She joined the Wuhan University of Science and Technology in 1994, where she is currently an Associate Professor with the Department of Automation. Her current research interests include signal processing and machine learning, fault detection, and multi-agent systems.

Jianliang Chen

Jianliang Chen received the M.S. degree in signal and information processing from Harbin Engineering University, Harbin, China, in 2004 and the Ph.D. degree in control science and engineering from the Wuhan University of Science and Technology, Wuhan, China, in 2013. He was a Post-Doctoral Fellow with Shanghai Jiao Tong University, Shanghai, China. He joined the Wuhan University of Science and Technology in 2004, where he is currently an Associate Professor with the Department of Automation. His current research interests include robust and nonlinear control, fault detection, and multi-agent systems.

Hongjun Chu

Hongjun Chu received the M.S. degree in applied mathematics from Wenzhou University, Wenzhou, China, in 2009 and the Ph.D. degree in control science and engineering from Shanghai Jiao Tong University, Shanghai, China, in 2017.He is currently with the Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing, China. His current research interest includes distributed control and optimization and their application into smart grid.

Juan Li

Juan Li received the Ph.D. degree in control science and engineering from the Wuhan University of Science and Technology in 2016, now she is a lecturer in Wuhan University of Science and Technology. Her main research interests include image processing and machine learning.