Global finite-time observers for a class of nonlinear systems

Yunyan Li; Yanjun Shen; Xiao Hua Xia

Kybernetika (2013)

  • Volume: 49, Issue: 2, page 319-340
  • ISSN: 0023-5954

Abstract

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Global finite-time observers are designed for a class of nonlinear systems with bounded varying rational powers imposed on the increments of the nonlinearities whose solutions exist and are unique for all positive time. The global finite-time observers designed in this paper are with two homogeneous terms. The global finite-time convergence of the observation error system is achieved by combining global asymptotic stability and local finite-time stability.

How to cite

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Li, Yunyan, Shen, Yanjun, and Xia, Xiao Hua. "Global finite-time observers for a class of nonlinear systems." Kybernetika 49.2 (2013): 319-340. <http://eudml.org/doc/260740>.

@article{Li2013,
abstract = {Global finite-time observers are designed for a class of nonlinear systems with bounded varying rational powers imposed on the increments of the nonlinearities whose solutions exist and are unique for all positive time. The global finite-time observers designed in this paper are with two homogeneous terms. The global finite-time convergence of the observation error system is achieved by combining global asymptotic stability and local finite-time stability.},
author = {Li, Yunyan, Shen, Yanjun, Xia, Xiao Hua},
journal = {Kybernetika},
keywords = {global finite-time observer; nonlinear system; homogeneity; global finite-time observer; nonlinear system; homogeneity},
language = {eng},
number = {2},
pages = {319-340},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Global finite-time observers for a class of nonlinear systems},
url = {http://eudml.org/doc/260740},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Li, Yunyan
AU - Shen, Yanjun
AU - Xia, Xiao Hua
TI - Global finite-time observers for a class of nonlinear systems
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 2
SP - 319
EP - 340
AB - Global finite-time observers are designed for a class of nonlinear systems with bounded varying rational powers imposed on the increments of the nonlinearities whose solutions exist and are unique for all positive time. The global finite-time observers designed in this paper are with two homogeneous terms. The global finite-time convergence of the observation error system is achieved by combining global asymptotic stability and local finite-time stability.
LA - eng
KW - global finite-time observer; nonlinear system; homogeneity; global finite-time observer; nonlinear system; homogeneity
UR - http://eudml.org/doc/260740
ER -

References

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  1. Bestle, D., Zeitz, M., 10.1080/00207178308933084, Internat. J. Control 38 (1983), 419-431. MR0708425DOI10.1080/00207178308933084
  2. Bhat, S. P., Bernstein, D. S., 10.1137/S0363012997321358, SIAM J. Control Optim. 38 (2000), 751-766. MR1756893DOI10.1137/S0363012997321358
  3. Bhat, S. P., Bernstein, D. S., 10.1007/s00498-005-0151-x, Math. Control Sign. Systems 17 (2005), 101-127. Zbl1110.34033MR2150956DOI10.1007/s00498-005-0151-x
  4. Chen, M. S., Chen, C. C., 10.1109/TAC.2007.910724, IEEE Trans. Automat. Control 52 (2007), 2365-2369. MR2374276DOI10.1109/TAC.2007.910724
  5. Engel, R., Kreisselmeier, G., 10.1109/TAC.2002.800673, IEEE Trans. Automat. Control 47 (2002), 1202-1204. MR1911500DOI10.1109/TAC.2002.800673
  6. Gauthier, J. P., Hammouri, H., Othman, S., 10.1109/9.256352, IEEE Trans. Automat. Control 37 (1992), 875-880. Zbl0775.93020MR1164571DOI10.1109/9.256352
  7. Hammouri, H., Targui, B., Armanet, F., 10.1002/rnc.638, Internat. J. Robust Nonlinear Control 12 (2002), 497-518. Zbl1006.93007MR1895967DOI10.1002/rnc.638
  8. Hong, Y., Xu, Y., Huang, J., 10.1016/S0167-6911(02)00130-5, Systems Control Lett. 46 (2002), 243-253. MR2010242DOI10.1016/S0167-6911(02)00130-5
  9. Kotta, Ü., 10.1016/0167-6911(87)90086-7, Systems Control Lett. 8 (1987), 453-457. Zbl0634.93039DOI10.1016/0167-6911(87)90086-7
  10. Krener, A. J., Isidori, A., Linearization by output injection and nonlinear observers., Syst.ems Control Lett. 3 (1983), 47-52. Zbl0524.93030MR0713426
  11. Krishnamurthy, P., Khorrami, F., Chandra, R. S., 10.1109/TAC.2003.820226, IEEE Trans. Automat. Control 48 (2003), 2277-2284. MR2027259DOI10.1109/TAC.2003.820226
  12. Levine, J., Marino, R., 10.1016/0167-6911(86)90019-8, Systems Control Lett. 7 (1986), 133-142. MR0836303DOI10.1016/0167-6911(86)90019-8
  13. Li, J., Qian, C., Frye, M. T., 10.1002/rnc.1401, Internat. J. Robust Nonlinear Control 19 (2009), 1697-1720. MR2553558DOI10.1002/rnc.1401
  14. Ménard, T., Moulay, E., Perruquetti, W., 10.1109/TAC.2010.2045698, IEEE Trans. Automat. Control 55 (2010), 1500-1506. MR2668964DOI10.1109/TAC.2010.2045698
  15. Moulay, E., Perruquetti, W., 10.1016/j.jmaa.2005.11.046, J. Math. Anal. Appl. 323 (2006), 1430-1443. Zbl1131.93043MR2260193DOI10.1016/j.jmaa.2005.11.046
  16. Moulay, E., Perruquetti, W., 10.1080/00207170701650303, Internat. J. Control 81 (2008), 797-803. Zbl1152.34353MR2406886DOI10.1080/00207170701650303
  17. Perruquetti, W., Floquet, T., Moulay, E., 10.1109/TAC.2007.914264, IEEE Trans. Automat. Control 53 (2008), 356-360. MR2391590DOI10.1109/TAC.2007.914264
  18. Pertew, A. M., Marquez, H. J., Zhao, Q., 10.1109/TAC.2006.878784, IEEE Trans. Automat. Control 51 (2006), 1211-1216. MR2239562DOI10.1109/TAC.2006.878784
  19. Praly, L., 10.1109/TAC.2003.812819, IEEE Trans. Automat. Control 48 (2003), 1103-1108. MR1986287DOI10.1109/TAC.2003.812819
  20. Raghavan, S., Hedrick, J. K., 10.1080/00207179408923090, Internat. J. Control 59 (1994), 515-528. Zbl0802.93007MR1261285DOI10.1080/00207179408923090
  21. Rajamani, R., 10.1109/9.661604, IEEE Trans. Automat. Control 43 (1998), 397-401. Zbl0905.93009MR1614812DOI10.1109/9.661604
  22. Rosier, L., 10.1016/0167-6911(92)90078-7, Systems Control Lett. 19 (1992), 467-473. Zbl0762.34032MR1195304DOI10.1016/0167-6911(92)90078-7
  23. Shen, Y., Huang, Y., 10.1109/TAC.2009.2029298, IEEE Trans. Automat. Control 54 (2009), 2621-2625. MR2571925DOI10.1109/TAC.2009.2029298
  24. Shen, Y., Xia, X., 10.1016/j.automatica.2008.05.015, Automatica 44 (2008), 3152-3156. Zbl1153.93332MR2531419DOI10.1016/j.automatica.2008.05.015
  25. Shen, Y., Xia, X., Semi-global finite-time observers for a class of non-Lipschitz systems., In: Nolcos, Bologna 2010, pp. 421-426. 
  26. Shen, Y., Xia, X., Global asymptotical stability and global finite-time stability for nonlinear homogeneous systems., In: 18th IFAC World Congress, Milan 2011, pp. 4644-4647. 
  27. Thau, F. E., 10.1080/00207177308932395, Internat. J. Control 17 (1973), 471-479. DOI10.1080/00207177308932395
  28. Venkataraman, S. T., Gulati, S., Terminal slider control of nonlinear systems., In: Proc. IEEE International Conference of Advanced Robotics, Pisa 1990, pp. 2513-2514. 
  29. Xia, X., Gao, W., 10.1137/0327011, SIAM J. Control Optim. 27 (1989), 199-216. Zbl0667.93014MR0980230DOI10.1137/0327011
  30. Zeitz, M., 10.1016/0167-6911(87)90021-1, Systems Control Lett. 9 (1987), 149-156. Zbl0624.93012MR0906234DOI10.1016/0167-6911(87)90021-1

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