Park, Ju H.; Kwon, O. M. Guaranteed cost control of time-delay chaotic systems. (English) Zbl 1102.37305 Chaos Solitons Fractals 27, No. 4, 1011-1018 (2006). 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. Cited in 24 Documents 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 Keywords:cost control problem; chaotic systems; memory state feedback controllers; Lyapunov method Software:LMI toolbox PDFBibTeX XMLCite \textit{J. H. Park} and \textit{O. M. Kwon}, Chaos Solitons Fractals 27, No. 4, 1011--1018 (2006; Zbl 1102.37305) Full Text: DOI 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.