This study concentrates on investigating the robust filtering problem for a nonlinear system described by a Takagi–Sugeno fuzzy model with distributed delay and time-varying delay. The stochastic distribution characteristic of the network-induced delay is considered, and the Bernoulli distributed sequence is utilized to represent the probability distribution of the delay appearing in certain intervals. Firstly, according to parallel distributed compensation, an augmented system with stochastic variable is established. Next, the performance criterion guaranteeing the mean-square asymptotic stability of the fuzzy filtering error system is formulated, by taking advantage of a novel Lyapunov–Krasovskii function and the integral inequality method. Thirdly, the robust filtering problem is converted into a convex optimization problem and solved using the linear matrix inequality technique. Finally, the results are provided by numerical simulation to certify the effectiveness of the designed filter.
AggarwalARawatTKKumarMet al. (2015) Optimal design of FIR high pass filter based on L1 error approximation using real coded genetic algorithm. Engineering Science and Technology, An International Journal18(4): 594–602.
2.
CaoYFrankPM (2000) Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Transactions on Fuzzy Systems8(2): 200–211.
3.
DongYHanQLamJ (2005) Network-based robust H∞ control of systems with uncertainty. Automatica41(6): 999–1007.
4.
DongYTianEZhangYet al. (2009) Delay-distribution-dependent robust stability of uncertain systems with time-varying delay. International Journal of Robust and Nonlinear Control19(4): 377–393.
5.
GaoHMengXChenT (2008) A parameter-dependent approach to robust H∞ filtering for time-delay systems. IEEE Transactions on Automatic Control53(10): 2420–2425.
6.
JiaXZhangDHaoXet al. (2009) Fuzzy H∞ tracking control for nonlinear networked control systems in T–S fuzzy model. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)39(4): 1073–1079.
7.
LiJWangHONiemannaDet al. (2000) Dynamic parallel distributed compensation for Takagi–Sugeno fuzzy systems: An LMI approach. Information Sciences123(3-4): 201–221.
8.
LiYZhangQLuoX (2016) Robust L1 dynamic output feedback control for a class of networked control systems based on T–S fuzzy model. Neurocomputing197: 86–94.
9.
LiuJGuZTianEet al. (2012) New results on H∞ filter design for nonlinear systems with time-delay through a T–S fuzzy model approach. International Journal of Systems Science43(3): 426–442.
10.
MaoX (2002) Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Transactions on Automatic Control47(10): 1604–1612.
11.
QiuJDingSXGaoHet al. (2016a) Fuzzy-model-based reliable static output feedback H∞ control of nonlinear hyperbolic PDE systems. IEEE Transactions on Fuzzy Systems24(2): 388–400.
12.
QiuJGaoHDingSX (2016b) Recent advances on fuzzy-model-based nonlinear networked control systems: A survey. IEEE Transactions on Industrial Electronics63(2): 1207–1217.
13.
ShenHXuYDickinsonBT (2014) Micro air vehicle’s attitude control using real-time pressure and shear information. Journal of Aircraft51(2): 661–671.
14.
ShiPLuanXLiuF (2012) H∞ filtering for discrete-time systems with stochastic incomplete measurement and mixed delays. IEEE Transactions on Industrial Electronics59(6): 2732–2739.
15.
ShiPZhangYChadliMet al. (2016) Mixed H∞ and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. IEEE Transactions on Neural Networks and Learning Systems27(4): 903–909.
16.
VidyasagarM (1986) Optimal rejection of persistent bounded disturbances. IEEE Transactions on Automatic Control31(6): 527–534.
17.
WangTQiuJFuSet al. (2017) Distributed fuzzy H∞ filtering for nonlinear multirate networked double-layer industrial processes. IEEE Transactions on Industrial Electronics64(6): 5203–5211.
18.
WangTQiuJGaoHet al. (2016) Network-based fuzzy control for nonlinear industrial processes with predictive compensation strategy. IEEE Transactions on Systems, Man, and Cybernetics: Systems (99): 1–11.
19.
WattsS (2012) Modeling and simulation of coherent sea clutter. IEEE Transactions on Aerospace and Electronic Systems48(4): 3303–3317.
20.
WuLWangZ (2009) Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay. Signal Processing89(9): 1739–1753.
21.
WuZShiPSuH (2012) Reliable control for discrete-time fuzzy systems with infinite-distributed delay. IEEE Transactions on Fuzzy Systems20(1): 22–31.
22.
XiaJXuSSongB (2007) Delay-dependent L2 − L∞ filter design for stochastic time-delay systems. Systems & Control Letters56(9–10): 579–587.
23.
YangFWangZHungYS (2002) Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises. IEEE Transactions on Automatic Control47(7): 1179–1183.
24.
YangFWangZHungYSet al. (2006) H∞ control for networked systems with random communication delays. IEEE Transactions on Automatic Control51(3): 511–518.
25.
YangHQianFYangFet al. (2016) H∞ filtering for nonlinear networked systems with randomly occurring distributed delays, missing measurements and sensor saturation. Information Sciences370–371: 772–782.
26.
ZhangDShiPWangQet al. (2017) Analysis and synthesis of networked control systems: A survey of recent advances and challenges. ISA Transactions66: 376–392.
27.
ZhangLGaoHKaynakO (2013) Network-induced constraints in networked control systems – a survey. IEEE Transactions on Industrial Informatics9(1): 403–416.
28.
ZhaoJWangJParkJHet al. (2015) Memory feedback controller design for stochastic markov jump distributed delay systems with input saturation and partially known transition rates. Nonlinear Analysis: Hybrid Systems15: 52–62.
29.
ZhengFFrankPM (2002) Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. International Journal of Robust and Nonlinear Control38(3): 487–497.
30.
ZhuSHanQZhangC (2014) l1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach. Automatica50(8): 2098–2107.
