Robust set-membership filtering for two-dimensional systems with sensor saturation under the Round-Robin protocol

Abstract

In this paper, the set-membership filtering problem is investigated for a class of polytopic uncertain two-dimensional shift-varying systems with delays and sensor saturation. The measurement information is transmitted between the sensors and the filter through a shared communication network. To avoid data congestions, the Round-Robin (R-R) protocol is employed to regulate the data transmission order. This paper aims to design a robust set-membership filter such that the real system states are always contained in the state estimate ellipsoid in the presence of the state delays, the sensor saturation, the parameter uncertainties, the R-R protocol and the unknown-but-bounded external perturbations. By using the mathematical induction, sufficient condition for the existence of the desired robust set-membership filter is given in the form of recursive linear matrix inequalities, and a convex optimisation method is also proposed to determine the optimal state estimation ellipsoid in the trace sense. One numerical example is also given to illustrate effectiveness of the proposed filtering strategy.

Keywords:

• Two-dimensional systems
• set-membership filtering
• Round-Robin protocol
• parameter uncertainties

Data availability statement

Data sharing is not applicable to this article as it describes entirely theoretical research.

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Key Research and Development Program of China under [grant number 2018AAA0100202], in part by the National Natural Science Foundation of China under [grant number 61903082], and in part by the Postgraduate Research & Practice Innovation Programof Jiangsu Province under [grant number KYCX21_0075].

Notes on contributors

Meiyu Li

Meiyu Li received her B.Sc. degree in Mathematics and Applied Mathematics from Dezhou University, Dezhou, China, in 2016, and the M.Sc. degree in Systems Science from Liaocheng University, Liaocheng, China, in 2019. From 2019, she is pursuing a Ph.D. degree from Southeast University, Nanjing, China. Her current research interests include 2-D systems, set-membership filtering, etc.

Jinling Liang

Jinling Liang received the B.Sc. and M.Sc. degrees in Mathematics from Northwest University, Xi'an, China, in 1997 and 1999, respectively, and a Ph.D. degree in Applied Mathematics from Southeast University, Nanjing, China, in 2006. She is currently a Professor in the School of Mathematics, Southeast University. She has published around 90 papers in refereed international journals. Her current research interests include stochastic systems, complex networks, robust filtering and bioinformatics.

Fan Wang

Fan Wang received the B.Sc. degree in Mathematics from Hefei Normal University in 2012, and a Ph.D. degree in Applied Mathematics from Southeast University, Nanjing, China, in 2018. She has published several papers in refereed international journals. Her research interests include stochastic systems, optimal control and robust filtering.