This paper presents the stability result and switching law for the considered unforced Takagi–Sugeno time-delay fuzzy switched system. For controller design, the parallel distributed compensation method is adopted to design a fuzzy controller to stabilize the time-delay fuzzy switched system. In addition, the stability and stabilization conditions for the overall fuzzy control system are formulated by linear matrix inequalities. Finally, an example is utilized to demonstrate the effectiveness of the proposed schemes.
HespanhaJPLiberzonDSontagED. Nonlinear norm-observability notions and stability of switched systems. IEEE Trans Autom Control2005; 50(2): 154–168.
2.
LeeTCJiangZP. Uniform asymptotic stability of nonlinear switched systems with an application to mobile robots. IEEE Trans Autom Control2008; 53(5): 1235–1252.
3.
XuHTeoKLLiuX. Robust stability analysis of guaranteed cost control for impulsive switched systems. IEEE Trans Syst Man, Cybern B, 2008; 38(5): 1419–1422.
4.
FainshilLMargaliotMChiganskyP. On the stability of positive linear switched systems under arbitrary switching laws. IEEE Trans Autom Control, 2008; 54(4): 897–899.
5.
LiberzonDMorseAS. Basic problems in stability and design of switched systems. IEEE Control Syst Mag1999; 19: 59–70.
6.
MorseAS. Supervisory control of families of linear set-point controllers-part 1: exact matching. IEEE Trans Autom Control1996; 41(10): 1413–1431.
7.
AgrachevAALiberzonD. Lie-algebraic stability criteria for switched systems. SIAM J Control Opt2001; 41(1): 253–269.
8.
HofbaurMWWilliamsBC. Hybrid estimation of complex systems. IEEE Trans Syst, Man, Cybern B2004; 34(5): 2178–2191.
9.
ChengDGuoLHuanJ. On quadratic Lyapunov functions. IEEE Trans Autom Control2003; 48(5): 885–890.
10.
LiZGWenCYSohYC. Stabilization of a class of switched systems via designing switching laws. IEEE Trans Autom Control2001; 46(4): 665–670.
11.
DayawansaWPMartinCF. A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Trans Autom Control1999; 44(4): 751–760.
12.
SunZGeSSAnalysis and synthesis of switched linear control systems. Automatica2005; 41: 181–195.
13.
SkafidasEEvansRJSavkinAV. Stability results for switched controller systems. Automatica1999; 35: 553–556.
14.
HespanhaJPMorseAS. Stability of switched systems with average dwell-time. In: IEEE conference on decision and control, December 1999, pp.2655–2660.
15.
LuBWuF. Switching LPV control design using multiple parameter-dependent Lyapunov functions. Automatica2004; 40: 1973–1980.
16.
ZhaiGHuBYasudaK. Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach. Int J Syst Sci2001; 32: 1055–1061.
17.
DongJWangYYangGH. Control synthesis of continuous-time T–S fuzzy systems with local nonlinear models. IEEE Trans Fuzzy Syst2009; 39(5): 1245–1258.
18.
LiTHSTsaiSHLeeJZ. Robust fuzzy control for a class of uncertain discrete fuzzy bilinear systems. IEEE Trans Syst, Man, Cybern B2008; 38(2): 510–527.
19.
HuaCWangQGGuanX. Robust adaptive controller design for nonlinear time-delay systems via T–S fuzzy approach. IEEE Trans Fuzzy Syst2009; 17(3): 711–723.
20.
ChenCS. Self-organizing adaptive neural fuzzy control for electrically driven robot manipulators. Proc IMechE, Part I: J Systems and Control Engineering2008; 222(4): 231–246.
21.
LiTHSTsaiSH. T–S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems. IEEE Trans Fuzzy Syst2007; 15(3): 494–506.
22.
TanakaKWangHO. Fuzzy control systems design and analysis: A linear matrix inequality approach. New York: Wiley, 2001.
23.
ChenCS. Self-organizing adaptive neural fuzzy control for electrically driven robot manipulators. Proc IMechE, Part I: J Systems and Control Engineering2008; 222(4): 231–246.
24.
KuCCChangWJHuangPH. Passive fuzzy controller design for stochastic Takagi–Sugeno fuzzy systems with time-varying delay. Proc IMechE, Part I: J Systems and Control Engineering2011; 225(2): 241–257.
25.
DuHZhangN. Robust stability control of vehicle rollover subject to actuator time delay. Proc IMechE, Part I: J Systems and Control Engineering2008; 222(3): 163–174.
26.
ChenBLinXPTongSC. Observer-based stabilization of T-S fuzzy systems with input delay. IEEE Trans Fuzzy Syst2008; 16(3): 652–663.
27.
TsaiSH. Robust control for Van de Vusse reactor via T–S fuzzy bilinear scheme. Expert System with Applic2011; 38(5): 4935–4944.
28.
XuSLamJ. Robust control for uncertain discrete-time-delay fuzzy systems via output feedback controllers. IEEE Trans Fuzzy Syst2005; 13(1): 82–93.
29.
TsaiSHLiTHS. Robust fuzzy control of a class of fuzzy bilinear systems with time-delay. Chaos, Solitons and Fractals2009; 39(5): 82–93.
30.
ChangWJKuCCKuFC. Observer-feedback fuzzy control with passivity property for discrete-time affine Takagi-Sugeno fuzzy models. Proc IMechE, Part I: J Systems and Control Engineering2010; 224(4): 387–401.
31.
WicksMPeletiesPDeCarloR. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems. Eur J Control1998; 4(2): 140–147.
32.
ChiouJSWangCJChengCM. Stability analysis and controller design of the nonlinear switched systems via T-S discrete-time fuzzy model. Int J Fuzzy Syst2009; 11(4): 213–224.
33.
ChiouJSWangCC. Analysis and synthesis of switched nonlinear systems using the T–S fuzzy model. Appl Math Modelling2010; 34: 1467–1481.
