Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Controlled Synchronization of an Array of Nonlinear System with Time Delays

Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

Abstract:

In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330083

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 993

References:


[1] I.I. Blekhman, A.L. Fradkov, H. Nijmeijer, A.Y. Pogromsky, Systems & Control Letters, Vol. 31, pp. 299-305, 1997.
[2] C. Sarasola, F.J. Torrealdea, A. DAnjou, A. Moujahid, M. Grana, Int. J. Bifurc. & Chaos, Vol. 13, pp. 177-191, 2003.
[3] Y. Tao, H.S. Hui, Physical Review E, Vol. 65, pp. 1-7, 2002.
[4] A.L. Fradkov, H. Nijmeijer, A. Markov, Int. J. Bifurc. & Chaos, Vol. 10, pp. 2807 2813, 2000.
[5] A. Rodriguez-Angeles, H. Nijmeijer, IEEE Trans. Control Systems Tech., Vol. 12, pp. 542-554, 2004.
[6] S. Dong, J.K. Mills, IEEE Trans. Robot. Automa., Vol. 18, pp. 498-510, 2002.
[7] S.J. Chung and J.E. Slotine, Proc. of the 46th Conference on Dicision and Control, New Orleans, USA, 2007.
[8] K. Gu, V. Kharitonov, J. Chen, "Stability of time-delay systems," Birkhauser, 2003.
[9] V.A. Yakubovich, "S-procedure in nonlinear control theory," Vestnik Leningrad University, Vol. 1, pp. 62-77, 1971.
[10] K. Li, S. Guan, X. Gong, and C.H. Lai, Physics Letters A, Vol. 372, pp. 7133-7139, 2008.
[11] H. Huang, G. Heng, J. Cao, Nonlinear Dynamics, Vol. 57, pp. 441-453, 2009.