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

作　　者：Shuangyun XING Feiqi DENG 

机构地区：[1]Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China [2]College of Science, Shenyang Jianzhu University, Shenyang 110168, China

出　　处：《Science China(Information Sciences)》2017年第12期89-106,共18页中国科学（信息科学）（英文版）

基　　金：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 People’s Republic of China(Grant No.2016K8-062);Shenyang Jianzhu University Discipline Content Education Project(Grant No.XKHY2-107)

摘　　要：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 H∞filter. The delay-dependent sufficient conditions are proposed to guarantee the systems to be regular, impulsefree, stochastically stable and to achieve a prescribed performance index ？γ. Finally, some simulation examples are proposed to manifest the effectiveness and merits of the filter design methodology developed in the paper.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 H∞filter. The delay-dependent sufficient conditions are proposed to guarantee the systems to be regular, impulsefree, stochastically stable and to achieve a prescribed performance index ？γ. Finally, some simulation examples are proposed to manifest the effectiveness and merits of the filter design methodology developed in the paper.

关 键 词：nonlinear stochastic singular systems dissipative filtering unknown membership functions stochastic admissibility time-varying delays 

分 类 号：O231[理学—运筹学与控制论]