In this paper, control of hyperchaotic Chen system is investigated under the existence of norm-bounded parameter uncertainties. A Takagi-Sugeno fuzzy model is employed to represent the hyperchaotic Chen system and the parallel distributed compensation technique is applied to design the time-delayed fuzzy state feedback controller. Based on Lyapunov stability theory, a sufficient delay-dependent or delay-independent stability criterion is given in term of linear matrix inequalities (LMIs) to guarantee the stability of the closed-loop system. The two sets of feedback gain matrices can be simultaneously obtained by solving a group of LMIs. Numerical simulation results demonstrate the effectiveness of the proposed method.
PyragasK.‘Continuous control of chaos by self-controlling feedback.’Phy. Lett. A170 (6) (1992): 421–428
2.
YanZ. Y.‘Controlling hyperchaos in the new hyperchaotic Chen system.’Appl. Math. Comput.168 (2) (2005): 1239–1250
3.
ParkJ. H.‘Adaptive synchronization of hyperchaotic Chen system with uncertain parameters.’Chaos, Solitons Fractals26 (3) (2005): 959–964
4.
HaeriM.DehghaniM.‘Impulsive synchronization of Chen's hyperchaotic system.’Phys. Lett. A356 (3) (2006): 226–230
5.
ZhangQ. J.LuJ. A.‘Passive control and synchronization of hyperchaotic Chen system.’Chin. Phys. B17 (2) (2008): 492–497
6.
El-DessokyM. M.‘Synchronization and anti-synchronization of a hyperchaotic Chen system.’Chaos, Solitons Fractals39 (4) (2009): 1790–1797
7.
TanakaK.IkedaT.WangH. O.‘A unified approach to controlling chaos via an LMI-based fuzzy control system design.’IEEE Trans. Circuits Syst. I: Fundam. Theory and Appl.45 (10) (1998): 1021–1040
8.
ChenC. L.GangF.GuanX. P.‘Robust synchronization of chaotic Lur'e systems via delayed feedback control.’Phy. Lett. A321 (2004): 344–354
9.
ChenC. L.GangF.GuanX. P.‘Parameter identification based synchronization for a class of chaotic systems with offset vector.’Phy. Lett. A330 (2004): 65–74
10.
WangY. W.GuanZ. H.WangH. O.XiaoJ. W.‘Impulsive control for T-S fuzzy system and its application to chaotic systems.’Int. J. Bifurcation Chaos Appl. Sci. Engng16 (8) (2006): 2417–2423
11.
KimJ.-H.HyunC.-H.KimE.ParkM.‘Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model.’IEEE Trans. Fuzzy Syst.15 (3) (2007): 359–369
12.
ZhongQ. S.BaoJ. F.YuY. B.LiaoX. F.‘Impulsive control for T-S fuzzy model-based chaotic systems.’Math. Comput. Simul.79 (3) (2008): 409–415
13.
WangY. W.GuanZ. H.WangH. O.‘LMI-based fuzzy stability and synchronization of Chen's system.’Phys. Lett. A320 (2-3) (2003): 154–159
14.
LiuX. W.GaoX.‘Delayed fuzzy controller design for hyperchaos with application to hyperchaotic Chen's system.’Int. J. Mod. Phys. C18 (7) (2007): 1095–1105
15.
LamH. K.LingW.-K.IuH. H.-C.LingS. S. H.‘Synchronization of chaotic systems using time-delayed fuzzy state-feedback controller.’IEEE Trans. Circuits Syst. I, Fundam. Theory Appl.55 (3) (2008): 893–903
ZhouX. B.WuY.LiY.XueH. Q.‘Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters.’Appl. Math. Comput.203 (1) (2008): 80–85
18.
LiY. X.TangW. K. S.ChenG. R.‘Generating hyperchaos via state feedback control.’Int. J. Bifurcation Chaos, Appl. Sci. Engng15 (10) (2005): 3367–3375
