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

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  • ReceivedMay 10, 2017
  • AcceptedJul 3, 2017
  • PublishedNov 9, 2017


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.


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).


[1] Wang Z, Ho D W C. Filtering on nonlinear time-delay stochastic systems. Automatica, 2003, 39: 101-109 CrossRef Google Scholar

[2] Deng F Q, Mao W H, Wan A H. A novel result on stability analysis for uncertain neutral stochastic time-varying delay systems. Appl Math Comput, 2013, 221: 132--143. Google Scholar

[3] Zhao X, Deng F. Moment stability of nonlinear discrete stochastic systems with time-delays based on -representation technique. Automatica, 2014, 50: 530-536 CrossRef Google Scholar

[4] Shengyuan Xu , Tongwen Chen . Robust H control for uncertain stochastic systems with state delay. IEEE Trans Automat Contr, 2002, 47: 2089-2094 CrossRef Google Scholar

[5] Mao X R. Stochastic Differential Equations and Their Applications. Chichester: Horwood, 1997. Google Scholar

[6] Hu J, Wang Z, Shen B. Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements. Int J Control, 2013, 86: 650-663 CrossRef Google Scholar

[7] Hu J, Wang Z, Liu S. A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements. Automatica, 2016, 64: 155-162 CrossRef Google Scholar

[8] Zhang J Y, Zhang Q L, Wang Y Y. A new design of sliding mode control for Markovian jump systems based on stochastic sliding surface. Inf Sci Int J, 2017, 391: 9--27. Google Scholar

[9] Liyi Dai . Filtering and LQG problems for discrete-time stochastic singular systems. IEEE Trans Automat Contr, 1989, 34: 1105-1108 CrossRef Google Scholar

[10] Darouach M, Boutayeb M, Zasadzinski M. Kalman filtering for continuous descriptor systems. Am Control Conf, 1997, 3: 2108--2112. Google Scholar

[11] Xing S, Zhang Q. Stability and exact observability of discrete stochastic singular systems based on generalised Lyapunov equations. IET Control Theor Appl, 2016, 10: 971-980 CrossRef Google Scholar

[12] Gao Z, Shi X. Observer-based controller design for stochastic descriptor systems with Brownian motions. Automatica, 2013, 49: 2229-2235 CrossRef Google Scholar

[13] Boukas E K. Stabilization of stochastic singular nonlinear hybrid systems. NOnlinear Anal-Theor Methods Appl, 2006, 64: 217-228 CrossRef Google Scholar

[14] Tseng C S. Robust fuzzy filter design for a class of nonlinear stochastic systems. IEEE Trans Fuzzy Syst, 2007, 15: 261-274 CrossRef Google Scholar

[15] Balasubramaniam P, Vembarasan V, Rakkiyappan R. Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays. Commun NOnlinear Sci Numer Simul, 2011, 16: 2109-2129 CrossRef ADS Google Scholar

[16] Muralisankar S, Manivannan A, Balasubramaniam P. Robust stability criteria for uncertain neutral type stochastic system with Takagi-Sugeno fuzzy model and Markovian jumping parameters. Commun NOnlinear Sci Numer Simul, 2012, 17: 3876-3893 CrossRef ADS Google Scholar

[17] Xing S, Zhang Q, Zhu B. Mean-square admissibility for stochastic T-S fuzzy singular systems based on extended quadratic Lyapunov function approach. Fuzzy Sets Syst, 2017, 307: 99-114 CrossRef Google Scholar

[18] Zhao F, Zhang Q, Yan X. $H_\infty~$ H filtering for stochastic singular fuzzy systems with time-varying delay. NOnlinear Dyn, 2015, 79: 215-228 CrossRef Google Scholar

[19] Yoneyama J. ${\mathrm{H}}_\infty$ output feedback control for fuzzy systems with immeasurable premise variables: discrete-time case. Appl Soft Comput, 2008, 160: 949--958. Google Scholar

[20] Li X J, Yang G H. Switching-type ${\mathrm{H}}_\infty$ filter design for T-S fuzzy systems with unknown or partially unknown membership functions. IEEE Trans Fuzzy Syst, 2013, 21: 385-392 CrossRef Google Scholar

[21] Ligang Wu , Daniel Ho . Fuzzy filter design for Itô stochastic systems with application to sensor fault detection. IEEE Trans Fuzzy Syst, 2009, 17: 233-242 CrossRef Google Scholar

[22] Li X J, Yang G H. Fault detection for T-S fuzzy systems with unknown membership functions. IEEE Trans Fuzzy Syst, 2014, 22: 139-152 CrossRef Google Scholar

[23] Zhu B Y, Zhang Q L, Zhao E L. Robust dissipative filtering for a kind of T-S fuzzy descriptor system with immeasurable premise variables. Int J Syst Sci, 2015, 47: 1--18. Google Scholar

[24] Dong J, Yang G H. $H_{\infty~}$ Filtering for Continuous-Time T-S Fuzzy Systems With Partly Immeasurable Premise Variables. IEEE Trans Syst Man Cybern Syst, 2017, 47: 1931-1940 CrossRef Google Scholar

[25] Su H Y, Ji X F, Chu J. Delay-dependent robust control for uncertain singular time-delay systems. Asian J Control, 2006, 8: 180--189. Google Scholar

[26] Ho D, Shi X, Wang Z, et al. Filtering for a class of stochastic descriptor systems. Dynam Cont Discrete Impulsive Syst, 2005, 2: 848--853. Google Scholar

[27] Huang L R, Mao X R. Stability of singular stochastic systems with Markovian switching. IEEE Trans Autom Control, 2011, 56: 273--277. Google Scholar

[28] Xu S Y, Lam J. Robust Control and Filtering of Singular Systems. Berlin: Springer, 2006. Google Scholar

[29] Fridman E. Stability of linear descriptor systems with delay: a Lyapunov-based approach. J Math Anal Appl, 2002, 273: 24-44 CrossRef Google Scholar

[30] Zhao X Y, Deng F Q. New-type stability theorem for stochastic functional differential equations with application to SFDSs with distributed delays. Int J Syst Sci, 2013, 45: 1156--1169. Google Scholar

[31] Marx B, Ragot J. Stability and $\textit{L}_{2}$-norm bound conditions for Takagi-Sugeno descriptor systems. In: Proceedings of the 17th IFAC World Congress, Seoul, 2008. 9976--9981. Google Scholar

[32] Boyd S, Vandenberghe L. Convex optimization with engineering applications. In: Lecture Notes. Stanford: Stanford University, 2001. Google Scholar

[33] Cao Y, Frank P M. Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans Fuzzy Syst, 2000, 2: 200--211. Google Scholar

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