Kybernetika 52 no. 3, 441-460, 2016

Globally uniformly ultimately bounded observer design for a class of nonlinear systems with sampled and delayed measurements

Daoyuan Zhang, Yanjun Shen and Xiaohua XiaDOI: 10.14736/kyb-2016-3-0441


In this paper, we consider two kinds of sampled-data observer design for a class of nonlinear systems. The system output is sampled and transmitted under two kinds of truncations. Firstly, we present definitions of the truncations and the globally uniformly ultimately bounded observer, respectively. Then, two kinds of observers are proposed by using the delayed measurements with these two truncations, respectively. The observers are hybrid in essence. For the first kind of observers, by constructing a Lyapunov-Krasovskii functional, sufficient conditions of globally uniformly ultimately bounded of the estimation errors are derived, and the maximum allowable sampling period and the maximum delay are also given. For the second ones, sufficient conditions are also given to ensure that the estimation errors are globally uniformly ultimately bounded. Finally, an example is provided to illustrate the design methods.


nonlinear systems, continuous observers, sampled output, delayed measurements


93C10, 93C57


  1. T. Ahmed-Ali and F. Lamnabhi-Lagarrigue: High gain observer design for some networked control systems. IEEE Trans. Automat. Control 57 (2012), 995-1000.   DOI:10.1109/tac.2011.2168049
  2. T. Ahmed-Ali, V. Van Assche, J. Massieu and P. Dorleans: Continuous-discrete observer for state affine systems with sampled and delayed measurements. IEEE Trans. Automat. Control 58 (2013), 1085-1091.   DOI:10.1109/tac.2012.2225555
  3. T. Ahmed-Ali, I. Karafyllis and F. Lamnabhi-Lagarrigue: Global exponential sampled-data observers for nonlinear systems with delayed measurements. Syst. Control Lett. 62 (2013), 539-549.   DOI:10.1016/j.sysconle.2013.03.008
  4. V. Andrieu, L. Praly and A. Astolfi: High gain observers with updated high-gain and homogeneous correction terms. Automatica 45 (2009), 422-428.   DOI:10.1016/j.automatica.2008.07.015
  5. M. Arcak and D. Nešić: A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation. Automatica 40 (2004), 1931-1938.   DOI:10.1016/j.automatica.2004.06.004
  6. E. Biyik and M. Arcak: A hybrid redesign of newton observers in the absence of an exact discrete-time model. Automatica 55 (2006), 429-436.   DOI:10.1016/j.sysconle.2005.09.005
  7. J. Gauthier, H. Hammouri and S. Othman: A simple observer for nonlinear systems applications to bioreactors. IEEE Trans. Automat. Control 37 (1992), 875-880.   DOI:10.1109/9.256352
  8. I. Karafyllis and C. Kravaris: From continuous time design to sampled-data design of observers. IEEE Trans. Automat. Control 54 (2009), 2169-2174.   DOI:10.1109/tac.2009.2024390
  9. Y. Li, Y. Shen and X. Xia: Global finite-time observers for a class of nonlinear systems. Kybernetika 49 (2013), 319-340.   CrossRef
  10. Y. Li, X. Xia and Y. Shen: A high-gain-based global finite-time nonlinear observer. Int. J. Control 86 (2013), 759-767.   DOI:10.1080/00207179.2012.760045
  11. Y. Liu, Z. Wang and X. Liu: On global exponential stability of generalized stochastic netural networks with mixed time-delays. Neurocomputing 70 (2006), 314-326.   DOI:10.1016/j.neucom.2006.01.031
  12. H. Nadri, H. Hammouri and R. Mota: Observer design for uniformly observable systems with sampled measurements. IEEE Trans. Automat. Control 58 (2013), 757-762.   DOI:10.1109/tac.2012.2212517
  13. L. Praly: Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate. IEEE Trans. Automat. Control 48 (2003), 1103-1108.   DOI:10.1109/tac.2003.812819
  14. Y. Shen and Y. Huang: Uniformly observable and globally lipschitzian nonlinear systems admit global finite-time observers. IEEE Trans. Automat. Control 54 (2009), 995-1006.   DOI:10.1109/tac.2009.2029298
  15. Y. Shen and X. Xia: Semi-global finite-time observers for nonlinear systems. Automatica 44 (2008), 3152-3156.   DOI:10.1016/j.automatica.2008.05.015
  16. V. Van Assche, T. Ahmed-Ali, C. Ham and F. Lamnabhi-Lagarrigue: High gain observer design for nonlinear systems with time varying delayed measurements. In: 18th IFAC World Congress, Milan 2011, pp. 692-696.   DOI:10.3182/20110828-6-it-1002.02421
  17. D. Zhang, Y. Shen and Y. Shen: Continuous observer design for nonlinear systems based on sampled output measurements. In: 33rd Chinese Control Conference, Nanjing 2014, pp. 3909-3914.   DOI:10.1109/chicc.2014.6895591
  18. D. Zhang, Y. Shen and X. Xia: Continuous observer design for nonlinear systems with sampled and delayed output measurements. In: 19th IFAC World Congress, Cape Town 2014, pp. 269-274.   DOI:10.3182/20140824-6-za-1003.00819