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Title: A separation principle for the stabilization of a class of time delay nonlinear systems (English)
Author: Benabdallah, Amel
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 51
Issue: 1
Year: 2015
Pages: 99-111
Summary lang: English
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Category: math
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Summary: In this paper, we establish a separation principle for a class of time-delay nonlinear systems satisfying some relaxed triangular-type condition. Under delay independent conditions, we propose a nonlinear time-delay observer to estimate the system states, a state feedback controller and we prove that the observer-based controller stabilizes the system. (English)
Keyword: delay system
Keyword: output feedback stabilization
Keyword: nonlinear observer
Keyword: separation principle
MSC: 93B17
MSC: 93C10
MSC: 93D15
MSC: 93D20
idZBL: Zbl 06433834
idMR: MR3333835
DOI: 10.14736/kyb-2015-1-0099
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Date available: 2015-03-23T18:51:51Z
Last updated: 2016-01-03
Stable URL: http://hdl.handle.net/10338.dmlcz/144204
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Reference: [1] Atassi, A. N., Khalil, H. K.: A separation principle for the stabilization of a class of nonlinear systems..IEEE Trans. Automat. Control 44 (1999), 1672-1687. Zbl 0958.93079, MR 1709863, 10.1109/9.788534
Reference: [2] Atassi, A. N., Khalil, H. K.: Separation results for the stabilization of nonlinear systems using different high-gain observer designs..Systems Control Lett. 39 (2000), 183-191. Zbl 0948.93007, MR 1831258, 10.1016/s0167-6911(99)00085-7
Reference: [3] Boyd, S., Ghaoui, L. El, Feron, E., Balakrishnan, V.: Linear matrix inequalities in systems and control theory..In: SIAM Stud. Appl. Math. 15 (1994). MR 1284712, 10.1137/1.9781611970777
Reference: [4] Choi, H. L., Lim, J. T.: Global exponential stabilization of a class of nonlinear systems by output feedback..IEEE Trans. Automat. Control 50 (2005), 2, 255-257. MR 2116434, 10.1109/tac.2004.841886
Reference: [5] Germani, A., Manes, C., Pepe, P.: Local asymptotic stability for nonlinear state feedback delay systems..Kybernetika 36 (2000), 31-42. Zbl 1249.93146, MR 1760886
Reference: [6] Germani, A., Manes, C., Pepe, P.: An asymptotic state observer for a class of nonlinear delay systems..Kybernetika 37 (2001), 459-478. Zbl 1265.93029, MR 1859096
Reference: [7] Germani, A., Manes, C., Pepe, P.: Input-output linearization with delay cancellation for nonlinear delay systems: the problem of the internal stability..Int. J. Robust Nonlinear Control 13 (2003), 909-937. Zbl 1039.93008, MR 1998320, 10.1002/rnc.853
Reference: [8] Germani, A., Manes, C., Pepe, P.: Separation theorems for a class of retarded nonlinear systems..In: IFAC-Papers OnLine, Workshop on Time-Delay Systems, Praha 2010. 10.3182/20100607-3-cz-4010.00006
Reference: [9] Germani, A., Manes, C., Pepe, P.: Observer-based stabilizing control for a class of nonlinear retarded systems..Lect. Notes Control Inform. Sci. 423 (2012), 331-342. Zbl 1298.93287, MR 3050770, 10.1007/978-3-642-25221-1_25
Reference: [10] Hale, J. K., Lunel, S. M.: Introduction to Functional Differential Equations. Applied Mathematical Sciences..Springer-Verlag, New York 1991. 10.1007/978-1-4612-4342-7
Reference: [11] Ibrir, S.: Observer-based control of a class of time-delay nonlinear systems having triangular structure..Automatica 47 (2011), 388-394. Zbl 1207.93015, MR 2878289, 10.1016/j.automatica.2010.10.052
Reference: [12] Jankovic, M.: Recursive predictor design for state and output feedback controllers for linear time delay systems..Automatica 46 (2010), 510-517. Zbl 1194.93077, MR 2877101, 10.1016/j.automatica.2010.01.021
Reference: [13] Khalil, H. K.: Nonlinear Systems..Prentice-Hall, Upper Saddle River, NJ 2001. Zbl 1194.93083, 10.1002/rnc.1054
Reference: [14] Kwon, O. M., Park, J. H., Lee, S. M., Won, S. C.: LMI optimization approach to observer-based controller design of uncertain time-delay systems via delayed feedback..J. Optim. Theory Appl. 128 (2006), 103-117. Zbl 1121.93025, MR 2201891, 10.1007/s10957-005-7560-3
Reference: [15] Li, X., Souza, C. de: Output feedback stabilization of linear time-delay systems. Stability and control of time-delay systems..Lect. Notes Control Inform. Sci. (1998), 241-258. MR 1482581, 10.1007/BFb0027489
Reference: [16] Marquez, L. A., Moog, C., Villa, M. Velasco: Observability and observers for nonlinear systems with time delay..Kybernetika 38 (2002), 445-456. MR 1937139
Reference: [17] Pepe, P., Karafyllis, I.: Converse Lyapunov-Krasovskii theorems for systems described by neutral functional differential equations in Hale's form..Int. J. Control 86 (2013), 232-243. Zbl 1278.93219, MR 3017700, 10.1080/00207179.2012.723137
Reference: [18] Qian, C., W.Lin: Output feedback control of a class of nonlinear systems: A non-separation principle paradigm..IEEE Trans. Automat. Control 47 (2002), 1710-1715. MR 1929946, 10.1109/tac.2002.803542
Reference: [19] Sun, Y. J.: Global stabilization of uncertain systems with time-varying delays via dynamic observer-based output feedback..Linear Algebra Appl. 353 (2002), 91-105. MR 1918750, 10.1016/s0024-3795(02)00292-6
Reference: [20] Thuan, M. V., Phat, V. N., Trinh, H.: Observer-based controller design of time-delay systems with an interval time-varying delay..Int. J. Appl. Math. Comput. Sci. 22 (2012), 4, 921-927. Zbl 1283.93057, MR 3059771, 10.2478/v10006-012-0068-8
Reference: [21] Tsinias, J.: A theorem on global stabilization of nonlinear systems by linear feedback..Systems Control Lett. 17 (1991), 357-362. Zbl 0749.93071, MR 1136537, 10.1016/0167-6911(91)90135-2
Reference: [22] Wang, Z., Goodall, D. P., Burnham, K. J.: On designing observers for time delay systems with nonlinear disturbances..Int. J. Control 75 (2002), 803-811. Zbl 1027.93007, MR 1924004, 10.1080/00207170210126245
Reference: [23] Zhang, X., and, Z. Cheng, Wang, X. P.: Output feedback stabilization of nonlinear systems with delayed output..In: Proc. American Control Conference, Portland 2005, pp. 4486-4490. 10.1109/acc.2005.1470769
Reference: [24] Zhou, L., Xiao, X., Lu, G.: Observers for a class of nonlinear systems with time delay..Asian J. Control 11 (2009), 6, 688-693. MR 2791315, 10.1002/asjc.150
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