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Guaranteed cost control of time-delay chaotic systems. (English) Zbl 1102.37305

Summary: This article studies a guaranteed cost control problem for a class of time-delay chaotic systems. Attention is focused on the design of memory state feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) framework, two criteria for the existence of the controller are derived in terms of LMIs. A numerical example is given to illustrate the method proposed.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D15 Stabilization of systems by feedback

Software:

LMI toolbox
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References:

[1] Mackey, M.; Glass, L., Science, 197, 287-289 (1977)
[2] Lu, H.; He, Z., IEEE Trans Circuit Syst, 43, 700-702 (1996)
[3] Tian, Y.; Gao, F., Physica D, 117, 1-12 (1998)
[4] Chen, G.; Yu, H., IEEE Trans Circuit Syst, 46, 767-772 (1999)
[5] Guan, X. P.; Chen, C. L.; Peng, H. P.; Fan, Z. P., Int J Bifurcat Chaos, 13, 193-205 (2003)
[6] Sun, J., Chaos, Solitons & Fractals, 21, 143-150 (2004)
[7] Park, J. H.; Kwon, O., Chaos, Solitons & Fractals, 23, 445-450 (2005)
[8] Ott, E.; Grebogi, C.; Yorke, J. A., Phys Rev Lett, 64, 1196-1199 (1990)
[9] Chang, S. S.L.; Peng, T. K.C., IEEE Trans Automat Control, 17, 474-483 (1979)
[10] Yu, L.; Gao, F., J Franklin Inst, 338, 101-110 (2001)
[11] Park, J. H., Appl Math Comput, 140, 523-535 (2003)
[12] Gu K. In: Proc IEEE CDC, Australia, December 2000. p. 2805-10.; Gu K. In: Proc IEEE CDC, Australia, December 2000. p. 2805-10.
[13] Yue, D.; Won, S., Electron Lett, 37, 992-993 (2001)
[14] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory (1994), SIAM: SIAM Philadelphia
[15] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., LMI control toolbox user’s guide (1995), The Mathworks: The Mathworks Massachusetts
[16] Hale, J.; Verduyn Lunel, S. M., Introduction to functional differential equations (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002
[17] Shobukhov, A., Int J Bifurcat Chaos, 8, 1347-1354 (1998)
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