This paper addresses local H∞ control method to reject the disturbance for continuous-time T-S fuzzy models. Firstly, in order to overcome a few drawbacks of the previous results such as the special structure of free variable, redundant restrictive conditions and parameters, the time derivatives of the membership functions are analyzed and new linear matrix inequalities are obtained. Secondly, the H∞ control theorem is obtained based on the new conditions. Finally, two examples are given to illustrate the effectiveness of the results.
LamH.K. and LeungF.H.F., LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno’s form, IEEE Trans Syst Man Cybern B Cybern37(5) (2008), 1396–1406.
2.
GuerraT.M. and BernalM., Strategies to exploit non-quadratic local stability analysis, Int J Fuzzy Syst14(3) (2012), 372–379.
3.
VafamandN. and SadeghiM.S., More relaxed stability conditions for fuzzy TS control systems by optimal determination of membership function information, Control Engineering & Applied Informatics16(2) (2014), 67–77.
4.
DongJ.X., YangG.H. and ZhangH.G., Stability analysis of T-S fuzzy control systems by using set theory, IEEE Trans Fuzzy Syst23(4) (2015), 827–841.
5.
SuX., ZhouH. and SongY.D., An Optimal Divisioning Technique to Stabilization Synthesis of T-S Fuzzy Delayed Systems, IEEE Trans Cybern47(5) (2017), 1147–1156.
6.
XieX.P., YueD., ZhangH.G. and PengC., Control synthesis of Discrete-Time T-S fuzzy systems: Reducing the conservatism whilst alleviating the computational burden, IEEE Transactions on Cybern47(9) (2017), 2480–2491.
7.
VafamandN. and SadeghiM.S., More Relaxed Non-Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties, Asian Journal of Control19(2) (2017), 467–481.
8.
LiH.Y., WangY., YaoD. and LuR., A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems, Automatica97 (2018), 404–413.
9.
LamH.K., A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis, Engineering Applications of Artificial Intelligence67 (2018), 390–408.
10.
LiH.Y., WangY., YaoD. and LuR., Adaptive finite-time tracking control of full states constrained nonlinear systems with dead-zone, Automatica100 (2019), 97–107.
11.
LiuY.J., GongM.Z., TongS.C., LiD.J. and GaoY., Fuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraint, IEEE Trans Fuzzy Syst24(5) (2016), 1147–1158.
12.
LiuY., BanX.J., WuF. and LamH.K., Gain-scheduling control of T-S fuzzy systems with actuator saturation, J Intelligent and Fuzzy Syst32(1) (2017), 2579–589.
13.
VafamandN. and RakhshanM., Dynamic Model-Based Fuzzy Controller for Maximum Power Point Tracking of Photovoltaic Systems: A Linear Matrix Inequality Approach, J Dyn Syst Measurement & Control139(5) (2017), 051010.
14.
WangJ.W., TsaiS.H., LiH.X. and LamH.K., Spatially piecewise fuzzy control design for sampled-data exponential stabilization of semilinear parabolic PDE systems, IEEE Trans Fuzzy Syst26(5) (2018), 2967–2980.
15.
LiH.Y., WangJ.H., WuL.G., LamH.K. and GaoY.B., Optimal guaranteed cost sliding-mode control of interval type-2 fuzzy time-delay systems, IEEE Trans Fuzzy Syst26(1) (2018), 246–257.
16.
WangJ.W., Dynamic boundary fuzzy control design of semilinear parabolic PDE systems with spatially noncollocated discrete observation, IEEE Trans Cybern49(8) (2019), 3041–3051.
17.
GuerraT.M., Estrada-ManzoV. and LendekZ., Observer design for Takagi-Sugeno descriptor models: An LMI approach, Automatica52 (2015), 154–159.
18.
XieX.P., YueD. and PengC., Observer design of Discrete-Time fuzzy systems based on an alterable weights method, IEEE Trans Cybern, 2018. DOI: 10.1109/TCYB.2018.2878419
19.
VuV.P. and WangW.J., Robust observer synthesis for the uncertain large-scale T-S fuzzy system, IET Control Theory Appl13(1) (2019), 134–145.
20.
MaH., ZhouQ., BaiL. and LiangH., Observer-based adaptive fuzzy fault-tolerant control for stochastic nonstrict-feedback nonlinear systems with input quantization, IEEE Trans on Syst Man Cybern49(2) (2019), 287–298.
21.
SuX.J., WuL.G., ShiP. and SongY.D., A novel approach to output feedback control of fuzzy stochastic systems, Automatica50(12) (2014), 3268–3275.
22.
LiY.M., TongS.C. and LiT.S., Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation, IEEE Trans on Cybern45(10) (2015), 2299–2308.
23.
LiY.M. and TongS.C., Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems, IEEE Trans on Cybern47(4) (2017), 1007–1016.
24.
HuaC.C., LiK. and GuanX.P., Adaptive fuzzy prescribed performance control for nonlinear switched Time-Delay systems with unmodeled dynamics, IEEE Trans Fuzzy Syst26(4) (2018), 1934–1945.
25.
LiuY.J., GongM.Z., TongS.C., ChenC.L.P. and LiD.J., Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints, IEEE Trans Fuzzy Syst26(5) (2018), 2607–2617.
26.
HuaC.C., LiK. and GuanX.P., Event-Based dynamic output feedback adaptive fuzzy control for stochastic nonlinear systems, IEEE Trans Fuzzy Syst26(5) (2018), 3004–3015.
27.
SuX.J., XiaF.Q., SongY.D., BasinM.V. and ZhaoL., l2-l∞ output feedback controller design for fuzzy systems over switching parameters, IEEE Trans Fuzzy Syst26(6) (2018), 3755–3769.
28.
VafamandN., AsemaniM.H. and KhayatianA., TS fuzzy robust L1 control for nonlinear systems with persistent bounded disturbances, J the Franklin Institute354(14) (2017), 5854–5876.
29.
VafamandN., AsemaniM.H. and KhayatianA., Robust L1 Observer-based Non-PDC Controller Design for Persistent Bounded Disturbed TS Fuzzy Systems, IEEE Trans Fuzzy Syst26(3) (2018), 1401–1413.
30.
TongS.C., ZhangL. and LiY., Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones, IEEE Trans Syst Man & Cybern. Syst46(1) (2017), 37–47.
31.
TongS.C., SunK.K. and SuiS., Observer-based adaptive fuzzy decentralized optimal control design for strict-feedback nonlinear large-scale systems, IEEE Trans Fuzzy Syst26(2) (2018), 569–584.
32.
TanakaK., IwasakiM. and WangH.O., A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Trans Fuzzy syst11(4) (2003), 582–589.
33.
MozelliL.A., PalharesR.M. and SouzaF.O., Reducing conservativeness in recent stability conditions of TS fuzzy systems, Automatica45(6) (2009), 1580–1583.
34.
ZhangH.G. and XieX.P., Relaxed Stability Conditions for Continuous-Time T-S Fuzzy-Control Systems Via Augmented Multi-Indexed Matrix Approach, IEEE Trans Fuzzy syst19(3) (2011), 478–492.
35.
LeeD.H., ParkJ.B. and JooY.H., A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi-Sugeno fuzzy systems, Inf Sci185(1) (2012), 230–248.
36.
FlariaF.A., SilvaG.N. and OliveiraV.A., Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions, Int J Syst Sci44(10) (2013), 1956–1969.
37.
XieX.P., LiuZ.W. and ZhuX.L., An efficient approach for reducing the conservatism of LMI-based stability conditions for continuous-time T-S fuzzy systems, Fuzzy Sets Syst263 (2015), 71–81.
38.
BernalM. and GuerraT.M., Generalized nonquadratic stability of continuous-time Takagi–Sugeno models, IEEE Trans Fuzzy syst18(4) (2010), 815–822.
39.
PanJ.T., GuerraT.M., FeiS.M. and JaadariA., Nonquadratic stabilization of continuous t-s fuzzy models: Lmi solution for a local approach, IEEE Trans Fuzzy Syst20(3) (2012), 594–602.
40.
MarquezR., GuerraT.M. and BernalM., Asymptotically necessary and sufficient conditions for Takagi-Sugeno models using generalized non-quadratic parameter-dependent controller design, Fuzzy Sets Syst306 (2017), 48–62.
41.
WangL.K. and LamH.K., A new approach to stability and stabilization analysis for continuous-time Takagi-Sugeno fuzzy systems with time delay,–, IEEE Trans Fuzzy syst26(4) (2465).
42.
WangL.K. and LamH.K., New stability criterion for continuous-time Takagi-Sugeno fuzzy systems with time-varying delay, IEEE Trans on Cybern49(4) (2019), 1551–1556.
43.
WangL.K. and LiuX.D., Local analysis of continuous-time Takagi-Sugeno fuzzy system with disturbances bounded by magnitude or energy: A Lagrange multiplier method, Inf Sci248 (2013), 89–102.
44.
WangL.K., PengJ.L. and LiuX.D., An approach to oberver design of continuous-time Takagi-Sugeno fuzzy model with bounded disturbances, Inf Sci324 (2015), 108–125.
45.
WangL.K., PengL.J., LiuD.X. and ZhangG.H., Further study on local stabilization of continuous-time nonlinear systems presented as takagi-sugeno fuzzy model, J Intelligent & Fuzzy Syst29(1) (2015), 283–292.
46.
WangY.Y., XieL.H. and de SouzaC.E., Robust control of a class of uncertain nonlinear systems, Syst Control Lett19(2) (1992), 139–149.
47.
TuanH., ApkarianP. and NarikiyoT., Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Trans Fuzzy Syst.9(2) (2001), 324–332.
48.
BernalM., Soto-CotaA., CortezJ., PitarchJ.L. and JaadariA., Local non-quadratic hh∞ control for continuous-time takagi-sugeno models, in: IEEE Int Conf Fuzzy Syst, IEEE, Taibei, China, 2011, 1615.1620.
