Reduced-order filtering for discrete-time singular systems under fading channels

Abstract

In this paper, the reduced-order ${\mathcal{H}}_{\mathrm{\infty }}$ filtering problem for discrete-time singular systems under fading channels is studied. Our aim is to design a reduced-order filter to ensure the filtering error system with fading measurements is stochastically admissible and meets the given performance index. And the designed method is less conservative. However, the standard linear matrix inequality (LMI) cannot be obtained due to the nonlinear terms in decoupling. For this purpose, a new LMI is obtained by using new decoupling method. Finally, numerical example and electrical circuit example are given to clearly illustrate that the proposed method is less conservative than that of the existing method.

Keywords:

• Discrete-time singular systems
• reduced-order filtering
• ${\mathcal{H}}_{\mathrm{\infty }}$ filtering
• fading channels
• conservative

Disclosure statement

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

Data availability statement

My paper has no associated data.

Notations

The notations used in this paper are standard. $\mathbb{E}$ means to find the expectation and $\mathbb{D}$ means to find the variance. $P^T$ and $P^{-1}$ are represented by the transpose and inverse of matrix P, respectively. $\mathrm{diag}\{\cdots \}$ stands for a block-diagonal matrix. ${\lambda }_{min}(\mathrm{\Lambda })$ and ${\lambda }_{max}(\mathrm{\Lambda })$ represent the minimum and maximum eigenvalues of the matrix Λ respectively. 0 represents proper dimensional zero matrix and I denotes the proper dimensional identity matrix.

Additional information

Funding

The work was supported in part by the Liaoning BaiQianWan Talents Program of China under Grant 2018049, in part by the Joint Project of Key Laboratory of Liaoning Province of China under Grant 2019-KF-03-12, and in part by the Science and Technology Research Project of Liaoning Provincial Education Department of China under Grant LJKZ1032.

Notes on contributors

Li-Juan Cai

Li-Juan Cai received the B.E. degree in applied mathematics from Shanxi Datong University, Datong, China, in 2019. She is currently working toward the M.S. degree in applied mathematics with the College of Mathematical Sciences, Bohai University, Jinzhou, China. Her research interests include control systems, singular systems.

Xiao-Heng Chang

Xiao-Heng Chang (M-11) received the B.E. and M.S. degrees from Liaoning Technical University, Fuxin, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, Shenyang, China, in 2007. He is currently a Professor with the College of Control Science and Engineering, Bohai University, Jinzhou, China, and is also a Professor with the Institute of Automation, Bohai University, Jinzhou, China. He is an author of the monographs Takagi-Sugeno Fuzzy Systems Non-fragile H? Filtering (Berlin Heidelberg, Springer, 2012) and Robust Output Feedback H? Control and Filtering for Uncertain Linear Systems (Berlin Heidelberg, Springer, 2014). His research interests include fuzzy control systems,networked control systems, and robust control. Prof. Chang is an Associate Editor of Applied Mathematics and Computation, International Journal of Control, Automation, and Systems, and Transactions of the Institute of Measurement and Control, and an Academic Editor of Mathematical Problems in Engineering. He is also an Editorial Board Member of International Journal of Modelling, Identification and Control.