×

zbMATH — the first resource for mathematics

Global finite-time observers for a class of nonlinear systems. (English) Zbl 1264.93029
Summary: 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 have 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.

MSC:
93B07 Observability
93C10 Nonlinear systems in control theory
93D20 Asymptotic stability in control theory
PDF BibTeX XML Cite
Full Text: Link
References:
[1] Bestle, D., Zeitz, M.: Cannonical form observer design for non-linear time-variable systems. Internat. J. Control 38 (1983), 419-431. · Zbl 0521.93012
[2] Bhat, S. P., Bernstein, D. S.: Finite-time stability of continous autonomous systems. SIAM J. Control Optim. 38 (2000), 751-766. · Zbl 0945.34039
[3] Bhat, S. P., Bernstein, D. S.: Geometric homogeneity with applications to finite-time stability. Math. Control Sign. Systems 17 (2005), 101-127. · Zbl 1110.34033
[4] Chen, M. S., Chen, C. C.: Robust nonlinear observer for Lipschitz nonlinear systems subject to disturbances. IEEE Trans. Automat. Control 52 (2007), 2365-2369. · Zbl 1366.93459
[5] Engel, R., Kreisselmeier, G.: A continuous-time observer which converges in finite time. IEEE Trans. Automat. Control 47 (2002), 1202-1204. · Zbl 1364.93084
[6] Gauthier, J. P., Hammouri, H., Othman, S.: A simple observer for nonlinear systems applications to bioreactors. IEEE Trans. Automat. Control 37 (1992), 875-880. · Zbl 0775.93020
[7] Hammouri, H., Targui, B., Armanet, F.: High gain observer based on a triangular structure. Internat. J. Robust Nonlinear Control 12 (2002), 497-518. · Zbl 1006.93007
[8] Hong, Y., Xu, Y., Huang, J.: Finite-time control for manipulators. Systems Control Lett. 46 (2002), 243-253. · Zbl 0994.93041
[9] Kotta, Ü.: Application of inverse system for linearization and decoupling. Systems Control Lett. 8 (1987), 453-457. · Zbl 0634.93039
[10] Krener, A. J., Isidori, A.: Linearization by output injection and nonlinear observers. Syst.ems Control Lett. 3 (1983), 47-52. · Zbl 0524.93030
[11] Krishnamurthy, P., Khorrami, F., Chandra, R. S.: Global high-gain-based observer and backstepping controller for generalized output-feedback canonical form. IEEE Trans. Automat. Control 48 (2003), 2277-2284. · Zbl 1364.93094
[12] Levine, J., Marino, R.: Nonlinear systems immersion, observers and finite dimensional filters. Systems Control Lett. 7 (1986), 133-142. · Zbl 0592.93030
[13] Li, J., Qian, C., Frye, M. T.: A dual-observer design for global output feedback stabilization of nonlinear systems with low-order and high-order nonlinearities. Internat. J. Robust Nonlinear Control 19 (2009), 1697-1720. · Zbl 1298.93274
[14] Ménard, T., Moulay, E., Perruquetti, W.: A global high-gain finite-time observer. IEEE Trans. Automat. Control 55 (2010), 1500-1506. · Zbl 1368.93052
[15] Moulay, E., Perruquetti, W.: Finite time stability and stabilization of a class of continuous systems. J. Math. Anal. Appl. 323 (2006), 1430-1443. · Zbl 1131.93043
[16] Moulay, E., Perruquetti, W.: Finite-time stability conditions for non-autonomous continuous systems. Internat. J. Control 81 (2008), 797-803. · Zbl 1152.34353
[17] Perruquetti, W., Floquet, T., Moulay, E.: Finite-time observers: application to secure communication. IEEE Trans. Automat. Control 53 (2008), 356-360. · Zbl 1367.94361
[18] Pertew, A. M., Marquez, H. J., Zhao, Q.: \(H_\infty\) observer design for Lipschitz nonlinear systems. IEEE Trans. Automat. Control 51 (2006), 1211-1216. · Zbl 1366.93162
[19] Praly, L.: Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate. IEEE Trans. Automat. Control 48 (2003), 1103-1108. · Zbl 1364.93718
[20] Raghavan, S., Hedrick, J. K.: Observer design for a class of nonlinear systems. Internat. J. Control 59 (1994), 515-528. · Zbl 0802.93007
[21] Rajamani, R.: Observers for Lipschitz nonlinear systems. IEEE Trans. Automat. Control 43 (1998), 397-401. · Zbl 0905.93009
[22] Rosier, L.: Homogeneous Lyapunov function for homogeneous continuous vector field. Systems Control Lett. 19 (1992), 467-473. · Zbl 0762.34032
[23] Shen, Y., Huang, Y.: Uniformly observable and globally Lipschitzian nonlinear systems admit global finite-time observers. IEEE Trans. Automat. Control 54 (2009), 2621-2625. · Zbl 1367.93097
[24] Shen, Y., Xia, X.: Semi-global finite-time observers for nonlinear systems. Automatica 44 (2008), 3152-3156. · Zbl 1153.93332
[25] Shen, Y., Xia, X.: Semi-global finite-time observers for a class of non-Lipschitz systems. Nolcos, Bologna 2010, pp. 421-426.
[26] Shen, Y., Xia, X.: Global asymptotical stability and global finite-time stability for nonlinear homogeneous systems. 18th IFAC World Congress, Milan 2011, pp. 4644-4647.
[27] Thau, F. E.: Observing the state of nonlinear dynamic systems. Internat. J. Control 17 (1973), 471-479. · Zbl 0249.93006
[28] Venkataraman, S. T., Gulati, S.: Terminal slider control of nonlinear systems. Proc. IEEE International Conference of Advanced Robotics, Pisa 1990, pp. 2513-2514.
[29] Xia, X., Gao, W.: Nonlinear observer design by observer error linearization. SIAM J. Control Optim. 27 (1989), 199-216. · Zbl 0667.93014
[30] Zeitz, M.: The extended Luenberger observer for nonlinear systems. Systems Control Lett. 9 (1987), 149-156. · Zbl 0624.93012
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.