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Impulsive stability of chaotic systems represented by T-S model. (English) Zbl 1198.34126
Summary: A novel and unified control approach that combines intelligent fuzzy logic methodology with impulsive control is developed for controlling a class of chaotic systems. We first introduce impulses into each subsystem of T-S fuzzy IF-THEN rules and then present a unified T-S impulsive fuzzy model for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by Lyapunov method techniques and a design procedure for estimating bounds on control matrices is also given. These results are shown to be less conservative than those existing ones in the literature and several numerical examples are presented to illustrate the effectiveness of this method.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34H10 Chaos control for problems involving ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
93C42 Fuzzy control/observation systems
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[1] Lian, K.Y.; Chiu, C.S., LMI-based fuzzy chaotic synchronization and communications, Fuzzy-IEEE, 9, 539-553, (2001)
[2] Wang HO, Tanaka K, Ikeda T. Fuzzy modeling and control of chaotic systems. In: Proc Fuzz-IEEE; 1996. p. 209-12.
[3] Tanaka, K.; Ikeda, T.; Wang, H.O., A unified approach to controlling chaos via an LMI-based fuzzy control system design, IEEE trans circuits syst I, 45, 1021-1040, (1998) · Zbl 0951.93046
[4] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans syst man cybernet, SMC-15, 116-132, (1985) · Zbl 0576.93021
[5] Ying, H., Sufficient conditions on uniform approximation of multivariate functions by general takagi – sugeno fuzzy systems with linear rule consequent, IEEE trans syst man cybernet A, 28, 4, 515-520, (1998)
[6] Gan, Q.; Harris, C.J., Fuzzy local linearization and local basis function expansion in nonlinear system modeling, IEEE trans syst man cybernet B, l29, 4, 559-565, (1999)
[7] Park, C.W.; Lee, C.H.; Park, M., Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty, Inform sci, 147, 245-266, (2002) · Zbl 1008.93512
[8] Wang, H.O.; Tanaka, K., An LMI-based stable fuzzy control of nonlinear systems and its application to control of chaos, Fuzzy-IEEE, 2, 1433-1438, (1996)
[9] Yang, T., Impulsive control, IEEE trans autom control, 44, 5, 1081-1083, (1999) · Zbl 0954.49022
[10] Li, C.; Liao, X., Complete and lag synchronization of hyerchaotic systems using small impulsive, Chaos, solitions & fractals, 22, 857-867, (2004) · Zbl 1129.93508
[11] Li, C.; Liao, X., Impulsive synchronization of nonlinear coupled chaotic systems, Phys lett A, 328, 7-50, (2004) · Zbl 1134.37367
[12] Xie, W.X.; Wen, C.Y.; Li, Z.G., Impulsive control for the stabilization and synchronization of Lorenz systems, Phys lett A, 275, 67-72, (2000) · Zbl 1115.93347
[13] Sun, J.T.; Zhang, Y.P.; Wu, Q.D., Impulsive control for the stabilization and synchronization of Lorenz systems, Phys lett A, 298, 153-160, (2002) · Zbl 0995.37021
[14] Chen; Yang, Q., Impulsive control and synchronization of unified chaotic system, Chaos, solitions & fractals, 20, 751-758, (2004) · Zbl 1050.93051
[15] Guan, Z.; Liao, R., On impulsive control and its application to chen’s chaotic system, Int J bifurcat chaos, 12, 5, 1191-1197, (2002) · Zbl 1051.93508
[16] Sun, J., Impulsive control of a new chaotic system, Math comput simulat, 64, 669-677, (2004) · Zbl 1076.65119
[17] Lu, J.A.; Wu, X.Q.; Lü, J.H., Synchronization of a unified system and the application in secure communication, Phys lett A, 305, 365-370, (2002) · Zbl 1005.37012
[18] Zhang, H.; Liao, X.; Yu, J., Fuzzy modeling and synchronization of hyperchaotic systems, Chaos, solitons & fractals, 26, 835-843, (2005) · Zbl 1093.93540
[19] Wang, J.; Xiong, X.; Zhao, M.; Zhang, Y.B., Fuzzy stability and synchronization of hyperchaos systems, Chaos, solitons & fractals, 35, 922-930, (2008) · Zbl 1136.93373
[20] Chen, B.; Liu, X.; Tong, S., Adaptive fuzzy approach to control unified chaotic systems, Chaos, solitons & fractals, 34, 1180-1187, (2007) · Zbl 1142.93356
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