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Delay-independent Stabilization of Linear Systems with Multiple Time-delays
Abstract:The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333278Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1495
 T. Amemiya, "Delay-independent stabilization of linear systems, " Int. J. Control, vol. 37, pp. 1071C1079, May 1983.
 K. Akazawa, T. Amemiya, and H. Tokumaru, "Further condition for the Delay-independent stabilization of linear systems, " Int. J. Control, vol. 46, pp.1195-1202, Aug. 1987.
 S. Y. Zhang, and L. Q. Gao, Modern control theory, Beijing: Tsinghua university press, 2006, ch. 6.
 R. Datko, "he stablization of linear functional differential equations, " in Calculus of Variations and Control Theory, D. L. Russel, Ed. New York : Academic Press, 1975, pp. 353-369.
 E. D. Kamen, "Linear systems with commensurate time delays: stability and stabilization independent of delay, " IEEE Transactions on Automatic Control, vol. 27, pp. 367-376, Feb. 1982.
 R. M. Lewis, and B. D. O. Anderson, "Necessary and sufficient conditions for delay-independent stability of linear autonomous systems, " IEEE Transactions on Automatic Control, vol. 25, pp.735-739, Aug. 1980.
 J. D. Zhu, "State feedback stabilization for linear discrete systems with transmission delays, " Control and Decision, vol. 23, pp. 651-654, 664, Jun. 2008.
 M. de la Sen, "On pole-placement controllers for linear for linear timedelay systems with commensurate point delays, " Mathematical Problems in Engineering, vol. 2005, pp.123C140, 2005
 E. Fridman, and U. Shaked, "An Improved Stabilization Method for Linear Time-Delay Systems, " IEEE Transactions on Automatic Control, vol. 47, pp.1931-1937, Nov. 2002.
 H. J. Cho, J. H. Park, and S. G. Lee, "Delay-dependent stabilization for time-delay systems: An LMI approach, " in International Conference on Control, Automation, and Systems, Thailand, 2004, pp. 1744-1746.
 W. Michiels, S. I. Niculescu, "Delay- independent stability and delay interference phenomena, " in Proceedings of the 17th International Symposium on Mathematical, Theory of Networks and Systems, Kyoto, Japan, 2006, pp. 2648-2659.
 Z. S. Feng, "Mean-square Asymptotic Stability Independent of Delay of Nonlinear Delay Ito Stochastic Systems, " Control and Decision, vol. 4, pp. 341-344, Jul. 1997.
 T. X. Y. Xu, Matrix Theory in Automatic Control, Beijing: Science press, 1979, ch. 9.
 L. H. Li, "The Application of Hamilton-Cayley Theorem, " Journal of Shanghai Power, vol. 24, pp. 192-194, Jun. 2008.
 T. A. Burton, "Uniform asymptotic stability in functional differential equations, " Proc. Amer. Math. Soc. vol. 68, pp. 195-199, 1978.