This paper investigates stability analysis and controller design for Takagi-Sugeno (T-S) fuzzy systems with stochastic time-varying delay (STVD). Considering the probabilistic characteristics of STVD, the initial systems are redesigned to novel configurations. An adaptive event-triggered control (AETC) strategy is employed to achieve stabilization for T-S fuzzy systems with STVD. An AETC is used to identify the appropriate triggering moments, which consequently reduces data transmission within Networked Control Systems (NCSs). A transient segmented Lyapunov-Krasovskii functional (LKF) is formulated by using a delay decomposition approach (DDA). The proposed LKF simultaneously incorporates three key parameters: time-varying delay upper bound, interval probability distributions, and delay derivative information. Stability criteria are formulated through the application of reciprocally convex techniques and integral inequalities. Unlike previous approaches, this paper improves STVD system analysis and design through a DDA with AETC integration. In conclusion, numerical simulations are used to show the feasibility of the established DDA.
TakagiTSugenoM.Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern1985; smc-15(1): 116–132.
2.
ZengHBZhuZJPengTS, et al. Robust tracking control design for a class of nonlinear networked control systems considering bounded package dropouts and external disturbance. IEEE Trans Fuzzy Syst2024; 32(6): 3608–3617.
3.
ZhangDCaiWXieL, et al. Nonfragile distributed filtering for T–S fuzzy systems in sensor networks. IEEE Trans Fuzzy Syst2015; 23(5): 1883–1890.
4.
ZhaoTHuangMDianS.Robust stability and stabilization conditions for nonlinear networked control systems with network-induced delay via T–S fuzzy model. IEEE Trans Fuzzy Syst2021; 29(3): 486–499.
5.
LiuXWuBWangY-E, et al. Quasi-time-dependent H∞ control for discrete-time switched systems with time-varying delay and unstable modes. Int J Control Autom Syst2024; 22: 1511–1525.
6.
LinHDongJParkJH.Robust H∞ control for uncertain T–S fuzzy systems with state and input time delays: A time-varying matrix-dependent zero-equality method. J Franklin Inst2024; 361(4): 106540.
7.
YuanSSDengWXYaoJY, et al. Robust control for bidirectional stabilization system with time delay estimation. Int J Control Autom Syst2024; 22: 1163–1175.
8.
LiuZLiuZJiangB, et al. Adaptive variable structure controller design for uncertain switched systems with unknown time-varying delay. Int J Control Autom Syst2023; 21: 3850–3859.
9.
ShaoHYuanGPangZ, et al. Stability of networked control systems: a Lyapunov-Krasovskii functional plus approach. ISA Trans2023; 136: 235–244.
10.
ZengHBZhaiZLHeY, et al. New insights on stability of sampled-data systems with time-delay. Appl Math Comput2020; 374: 125041.
11.
KuppusamySJooYH.Nonfragile retarded sampled-data switched control of T–S fuzzy systems and its applications. IEEE Trans Fuzzy Syst2020; 28(10): 2523–2532.
12.
LiHJingXLamH-K, et al. Fuzzy sampled-data control for uncertain vehicle suspension systems. IEEE Trans Cybern2014; 44(7): 1111–1126.
13.
GandhiVJooYH.T–S fuzzy sampled-data control for nonlinear systems with actuator faults and its application to wind energy system. IEEE Trans Fuzzy Syst2022; 30(2): 462–474.
14.
LiBWuJFHuangL. Improved H∞ control for networked control systems with network-induced delay and packet dropout. J Central South Univ2016; 23: 1215–1223.
15.
XiaoH-QHeYWuM, et al. New results on H∞ tracking control based on the T–S fuzzy model for sampled-data networked control system. IEEE Trans Fuzzy Syst2015; 23(6): 2439–2448.
16.
Lakehal AyatEHDMansouriNBoukabouA.Dynamic output feedback robust H∞ control of networked control systems with time-varying delays via T-S fuzzy models. J Franklin Inst2022; 359(15): 8127–8154.
17.
JiangXChenXHuangT, et al. Output tracking control of single-input-multioutput systems over an erasure channel. IEEE Trans Cybern2022; 52(4): 2609–2617.
18.
LiMChenY.Robust time-varying H∞ control for networked control system with uncertainties and external disturbance. Int J Control Autom Syst2018; 16: 2125–2135.
19.
DuZKaoYKarimiHR, et al. Interval type-2 fuzzy sampled-data H∞ control for nonlinear unreliable networked control systems. IEEE Trans Fuzzy Syst2020; 28(7): 1434–1448.
20.
ZhaoJLinCMHuangJ. Decentralized sampled-data control for continuous-time large-scale networked nonlinear systems. Int J Fuzzy Syst2017; 19: 504–515.
21.
PengGPengK.An H∞ output tracking control approach to sampled-data control for nonlinear networked control systems. IEEE Access2020; 8: 143644–143653.
22.
WangXParkJHYangH, et al. Delay-dependent fuzzy sampled-data synchronization of T–S fuzzy complex networks with multiple couplings. IEEE Trans Fuzzy Syst2020; 28(1): 178–189.
23.
HuZMuX.Mean square stabilization for sampled-data T–S fuzzy systems with random packet dropout. IEEE Trans Fuzzy Syst2020; 28(8): 1815–1824.
24.
WuYLuRShiP, et al. Sampled-data synchronization of complex networks with partial couplings and T–S Fuzzy nodes. IEEE Trans Fuzzy Syst2018; 26(2): 782–793.
25.
GeCLiuZWangL, et al. Improved stability criteria of T-S fuzzy systems with sampled-data-based dissipative control. Appl Math Comput2022; 424: 127047.
26.
LiY-XYangG-H.Observer-based fuzzy adaptive event-triggered control co-design for a class of uncertain nonlinear systems. IEEE Trans Fuzzy Syst2018; 26(3): 1589–1599.
27.
LiSAhnCKGuoJ, et al. Neural-network approximation-based adaptive periodic event-triggered output-feedback control of switched nonlinear systems. IEEE Trans Cybern2021; 51(8): 4011–4020.
28.
LiMLiSAhnCK, et al. Adaptive fuzzy event-triggered command-filtered control for nonlinear time-delay systems. IEEE Trans Fuzzy Syst2022; 30(4): 1025–1035.
29.
ZhangJLiSAhnCK, et al. Decentralized event-triggered adaptive fuzzy control for nonlinear switched large-scale systems with input delay via command-filtered backstepping. IEEE Trans Fuzzy Syst2022; 30(6): 2118–2123.
30.
YangYNiuY.Event-triggered adaptive neural backstepping control for nonstrict-feedback nonlinear time-delay systems. J Franklin Inst2020; 357(8): 4624–4644.
31.
ZhengYGaoSZhengW, et al. Fuzzy adaptive event-triggered control for uncertain nonlinear system with prescribed performance: a combinational measurement approach. J Franklin Inst2022; 359(1): 371–391.
32.
LiZYanHZhangH, et al. Aperiodic sampled-data Takagi–Sugeno fuzzy extended state observer for a class of uncertain nonlinear systems with external disturbance and unmodeled dynamics. IEEE Trans Fuzzy Syst2022; 30(7): 2678–2692.
33.
YanSGuZDingL, et al. Weighted memory H∞ stabilization of time-varying delayed Takagi–Sugeno fuzzy systems. IEEE Trans Fuzzy Syst2024; 32(1): 337–342.
34.
MuYZhangHSuH, et al. Robust normalization and stabilization for uncertain Takagi-Sugeno fuzzy singular systems with time-delays. Appl Math Comput2021; 388: 125534.
35.
FrezzattoLOliveiraRCLFPeresPLD. H∞ non-minimal filter design in finite frequency ranges for discrete-time Takagi–Sugeno fuzzy systems with time-varying delays. J Franklin Inst2020; 357(1): 622–634.
36.
WangX-LYangG-H.Event-triggered H∞ filtering for discrete-time T–S fuzzy system via network delay optimization technique. IEEE Trans Syst Man Cybern Syst2019; 49(10): 2026–2035.
37.
LiuJLiuQCaoJ, et al. Adaptive event-triggered H∞ filtering for T-S fuzzy system with time delay. Neurocomputing2016; 189: 86–94.
38.
Shamrooz AslamMQaisarIMajidA, et al. Adaptive event-triggered robust H∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time-varying delay. Asian J Control2023; 25(1): 213–228.
39.
GuoXGFanXAhnCK.Adaptive event-triggered fault detection for interval type-2 T–S fuzzy systems with sensor saturation. IEEE Trans Fuzzy Syst2021; 29(8): 2310–2321.
40.
YangYNiuYLamJ.Interval type-2 fuzzy sliding mode resilient control via probability-dependent adaptive event-triggered scheme. IEEE Trans Syst Man Cybern Syst2023; 53(6): 3474–3484.
41.
LuoJTianWZhongS, et al. Improved delay-probability-dependent results for stochastic neural networks with randomly occurring uncertainties and multiple delays. Int J Syst Sci2018; 49(9): 2039–2059.
42.
GuanXPChenCL.Delay-dependent guaranteed cost control for T–S fuzzy systems with time delays. IEEE Trans Fuzzy Syst2004; 12(2): 236–249.
43.
ParkPKoJWJeongC. Reciprocally convex approach to stability of systems with time-varying delays. Automatica2011; 47(1): 235–238.
