In this paper, a new method, namely, the dynamic delay partitioning method, is firstly developed to solve the problems of stability analysis and stabilization for a class of unknown nonlinear systems. To study the system stability and facilitate the design of fuzzy controller, Takagi-Sugeno (T-S) fuzzy models are employed to represent the system dynamics of the unknown nonlinear systems. Different from previous results, the delay interval [0, d (t)] is partitioned into some variable subintervals by employing dynamic delay partitioning method. Thus, new delay-dependent stability criteria for fuzzy time-delay systems is derived, which is less conservative than previous results. By the criteria, the approach to design a fuzzy controller is developed. Two examples are provided to demonstrate the effectiveness for conservatism reduction.
BrierleyS.D., ChiassonJ.N., LeeE.B. and ZakS.H., On stability independent of delay for linear systems, IEEE Transactions on Automatic Control27 (1982), 252–254.
2.
MahmoudM.S. and Al-MuthairiN.F., Design of robust controllers for time-delay systems, IEEE Transactions on Automatic Control39 (1994), 995–999.
3.
ZhangH.G. and XieX.P., Relaxed stability conditions for continuous-time T-S fuzzy-control systems via augmented multi-indexed matrix approach, IEEE Transactions on Fuzzy Systems19(3) (2011), 478–492.
4.
MozelliL.A., SouzaF.O. and PalharesR.M., A new discretized Lyapunov-Krasovskii functional for stability analysis and control design of time-delayed TS fuzzy systems, International Journal of Robust and Nonlinear Control21 (1) (2011), 93–105.
5.
LiuY., BanX.J., WuF. and LamH.K., Gain-scheduling control of T-S fuzzy systems with actuator saturation, Journal of Intelligent & Fuzzy Systems32 (2017), 2579–2589.
6.
SakthivelR., ShiP., ArunkumardA. and MathiyalagandK., Robust reliable H∞ control for fuzzy systems with random delays and linear fractional uncertainties, Fuzzy Sets and Systems302 (2016), 65–81.
7.
SakthivelR., SundareswariK., MathiyalaganK. and SantraS., Reliable H∞ stabilization of fuzzy systems with random delay via nonlinear retarded control, Circuits, Systems and Signal Processing35 (2016), 1123–1145.
8.
SakthivelR., SelviS., MathiyalaganK. and ShiP., Reliable mixed H∞ and passivity-based control for fuzzy markovian switching systems with probabilistic time delays and cctuator failures, IEEE Transactions on Cybernetics45 (2015), 2720–2731.
9.
ZhangH.G., LunS.X. and LiuD.R., Fuzzy H∞ filter design for a class of nonlinear discrete-time systems with multiple time delays, IEEE Transactions on Fuzzy Systems15 (3) (2007), 453–469.
10.
TsaiS.H., A global exponential fuzzy observer design for time-delay Takagi-Sugeno uncertain discrete fuzzy bilinear systems with disturbance, IEEE Transactions on Fuzzy Systems20 (6) (2012), 1063–1075.
11.
ZhangH.G., LiM., YanguJ. and YangD.D., Fuzzy modelbased robust networked control for a class of nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans39 (2) (2009), 437–447.
12.
HyunC.H., ParkuC.W. and KimS., Takagi-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design, Information Sciences180 (11) (2010), 2314–2327.
13.
HeY., LiuuG. and ReesD., New delay-dependent stability criteria for neural networks with time-varying delay, IEEE Transactions on Neural Networks18 (1) (2007), 310–314.
14.
WangG., ZhangH.G., ChenuB. and TongS.C., Fuzzy hyperbolic neural network with time-varying delays, Fuzzy Sets and Systems161 (2010), 2533–2551.
15.
LiT., GuoL., SunuC. and LinC., Further result on delaydependent stability criterion of neural networks with timevarying delays, IEEE Transactions on Neural Networks19 (4) (2008), 726–730.
16.
XiaoH., HeY., WuM., XiaouS. and SheJ., New results on H∞ tracking control for sampled-data networked control systems, IEEE Transactions on Fuzzy Systems23 (6) (2015), 2439–2448.
17.
ZhaoY., GaoH.J., LamuJ. and DuB.Z., Stability and stabilization of delayed T-S fuzzy systems: A delay partitioning approach, IEEE Transactions on Fuzzy Systems17 (4) (2009), 750–762.
18.
ZhaoL., GaouH.J. and KarimiH.R., Robust stability and stabilization of uncertain T-S fuzzy systems with time-varying delay: An input-output approach, IEEE Transactions on Fuzzy Systems21 (5) (2013), 883–897.
19.
TsaiS.H., ChenuY.A. and LoJ.C., A novel stabilization condition for a class of T-S fuzzy time-delay systems, Neurocomputing175 (2016), 223–232.
20.
ZhangZ.Y., LinuC. and ChenB., New stability and stabilization conditions for T-S fuzzy systems withtime delay, Fuzzy Sets and Systems263 (2015), 82–91.
21.
TakagiuT. and SugenoM., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man, and CyberneticsSMC-15 (1) (1985), 116–132.
22.
WanguH., TanakaK. and GriffinM., An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Transactions on Fuzzy Systems4 (1996), 14–23.
23.
RheeuB.J. and WonS., A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design, Fuzzy Sets and Systems157 (9) (2006), 1211–1228.
24.
LouJ.C., ZhangC.M., Relaxation analysis via line integral, in: Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, 1264–1269.
25.
WangY., XieuL.H. and DeC.E., Souza, Robust control of a class of uncertain nonlinear systems, Systems & Control Letters19 (2) (1992), 139–149.
26.
NelderJ.A. and MeadR., A simplex method for function minimization, Computer Journal7 (1965), 308–313.
