Generalised KYP lemma with its application in finite frequency H_∞ distributed filter design for nonideally interconnected networked control systems

Abstract

This paper addresses the generalised Kalman-Yakubovich-Popov (GKYP) lemma and its application in finite frequency (FF) $H_{\mathrm{\infty }}$ distributed filter design for networked control systems (NCSs). The network communication channels between subsystems are considered to be affected by uncertainties. Firstly, based on the proposed linear matrix inequality characterisation for an FF region and S-procedure, a GKYP lemma is presented for NCSs. After that, the FF bounded realness and FF positive realness in terms of individual subsystems are studied as special cases of the proposed GKYP lemma. Moreover, as an application of the developed GKYP lemma, the FF $H_{\mathrm{\infty }}$ distributed filtering problem for nonideally interconnected NCS is studied. Finally, illustrative examples are given to show that the developed EF methods have less conservation than the common method over the entire frequency region.

Keywords:

• Networked control system
• generalised Kalman-Yakubovich-Popov lemma
• finite frequency
• distributed filter

Disclosure statement

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

Additional information

Funding

This work is supported by National Natural Science Foundation of China under Grant 61673218 and Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant KYCX18_0376 and KYCX19_0253.

Notes on contributors

Xuefeng Chen

Xuefeng Chen received his B.S. degree in mathematics from Nanjing University of Science and Technology, China, in 2015, where he is currently pursuing the Ph.D. degree in Applied Mathematics. His current research interests include distributed control and filtering, finite frequency control, interconnected systems.

Huiling Xu

Huiling Xu received her B.S. degree in mathematics from the Nanjing University of Science and Technology, China in 1992, and the M.S. and Ph.D. degrees in control science and control engineering from the Nanjing University of Science and Technology, China in 1999 and 2005, respectively. From 2009 to 2011 she was a Research Fellow in the school of electrical and electronic engineering at the Nanyang Technological University (NTU), Singapore. Since Apr. 2012, she has been a Professor in the school of science at the Nanjing University of Science and Technology, China. Her current research interests include distributed control, multidimensional systems, singular systems, time-delay systems, modeling and optimization for big data analytics.

Xiaokai Zhai

Xiaokai Zhai received his B.S. degree in mathematics from Nanjing University of Science and Technology, China, in 2015, where he is currently pursuing the Ph.D. degree in Applied Mathematics. His current research interests include robust distributed control and filtering, finite frequency control, spatially interconnected systems.

Zhiping Lin

Zhiping Lin received the B. Eng. degree in control engineering from South China Institute of Technology, Canton, China in 1982 and the Ph.D. degree in information engineering from the University of Cambridge, England in 1987. He was with the University of Calgary, Canada for 1987-1988, with Shantou University, China for 1988-1993, and with DSO National Laboratories, Singapore for 1993-1999. Since 1999, he has been with Nanyang Technological University (NTU), Singapore. He is a Program Director at Centre for Bio Devices and Signal Analysis, NTU. Dr Lin was the Editor-in-Chief of Multidimensional Systems and Signal Processing for 2011-2015, after being in its editorial board since 1993. He was an Associate Editor of Circuits, Systems and Signal Processing for 2000-2007 and an Associate Editor of IEEE Transactions on Circuits and Systems-II for 2010-2011. He was a reviewer for Mathematical Reviews for 2011-2013. He is currently a Subject Editor and a Guest Editor of the Journal of the Franklin Institute. His research interests include multidimensional systems and signal processing, statistical and biomedical signal processing, and machine learning.