SCIENCE CHINA Information Sciences, Volume 60, Issue 12: 120208(2017) https://doi.org/10.1007/s11432-017-9163-4

## Delay-dependent dissipative filtering for nonlinear stochastic singular systems with time-varying delays

• AcceptedJul 3, 2017
• PublishedNov 9, 2017
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### Abstract

This paper concentrates on studying the delay-dependent dissipative filtering problem for nonlinear stochastic singular systems with time-varying delays via a Takagi-Sugeno (T-S) fuzzy control approach. The T-S fuzzy model is employed to represent a nonlinear stochastic singular system with unknown or partially unknown membership functions. Firstly, based on an auxiliary vector function, by utilizing an integral inequality and the free-weighting-matrix approach, a delay-dependent sufficient condition is derived to enable the considered filtering error system with time-varying delays to be stochastically admissible and dissipative. Furthermore, on the basis of the derived condition, by using a new type of candidate Lyapunov-Krasovskii function, the solvability conditions of the dissipative filter are addressed, and the corresponding fuzzy filter parameters can be obtained by solving a set of linear matrix inequalities. And then, we deduce the solving method for the ${\mathrm{H}}_\infty$ filter. The delay-dependent sufficient conditions are proposed to guarantee the systems to be regular, impulse-free, stochastically stable and to achieve a prescribed performance index $\hat{\gamma}$. Finally, some simulation examples are proposed to manifest the effectiveness and merits of the filter design methodology developed in the paper.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573156, 61733008, 61503142), Natural Science Foundation of Guangdong Province (Grant No. 2017A030313332), Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130172110027), Natural Science Foundation of Liaoning Province (Grant No. 201602604), Science Research Fund of Education Department of Liaoning Province (Grant No. L2014237), Ministry of Housing and Urban-Rural Development of the Peoples Republic of China (Grant No. 2016K8-062) and Shenyang Jianzhu University Discipline Content Education Project (Grant No. XKHY2-107).

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• Figure 1

(Color online) State responses of system (2).

• Figure 2

The trajectory of the dissipative filtering error.

• Figure 3

(Color online) The measured output and external disturbance of the filtering error system.

• Figure 4

The trajectory of the dissipative filtering error.

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