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Research Articles

New structure to design interval observers for linear continuous-time systems

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Pages 1638-1646 | Received 29 Aug 2022, Accepted 29 May 2023, Published online: 14 Jun 2023

References

  • Alefeld, G., & Mayer, G. (2000). Interval analysis: Theory and applications. Journal of Computational and Applied Mathematics, 121(1-2), 421–464. https://doi.org/10.1016/S0377-0427(00)00342-3
  • Avilés, J., & Moreno, J. (2014). Preserving order observers for nonlinear systems. International Journal of Robust and Nonlinear Control, 24(16), 2153–2178. https://doi.org/10.1002/rnc.2975
  • Bako, L., & Andrieu, L. (2019). Interval-valued state estimation for linear systems the tightest estimator and its relaxations. Automatica, 106, 168–177. https://doi.org/10.1016/j.automatica.2019.04.045
  • Chambon, E., Burlion, L., & Apkarian, P. (2016). Overview of linear time-invariant interval observer design: Towards a non-smooth optimisation-based approach. IET Control Theory & Applications, 10(11), 1258–1268. https://doi.org/10.1049/cth2.v10.11
  • Chambon, E., Burlion, L., & Apkarian, P. (2016). Overview of linear time-invariant interval observer design: Towards a non-smooth optimisation-based approach. IET Control Theory & Applications, 10(11), 1258–1268. https://doi.org/10.1049/cth2.v10.11
  • Efimov, D., Fridman, E., Polyakov, A., Perruquetti, W., & Richard, J. (2016). On design of interval observers with sampled measurement. Systems & Control Letters, 96, 158–164. https://doi.org/10.1016/j.sysconle.2016.08.002
  • Efimov, D., & Raïssi, T. (2016). Design of interval observers for uncertain dynamical systems. Automation and Remote Control, 77(2), 191–225. https://doi.org/10.1134/S0005117916020016
  • F. Mazenc, T. N. D., & Niculescu, S. I. (2014). Interval observers for discrete-time systems. International Journal of Robust and Nonlinear Control, 24(17), 2867–2890. https://doi.org/10.1002/rnc.3030
  • Goffaux, G., Remy, M., & Wouwer, A. (2013). Continuous–discrete confidence interval observer–application to vehicle positioning. Information Fusion, 14(4), 541–550. https://doi.org/10.1016/j.inffus.2013.02.006
  • Hadj-Sadok, M., & Gouzé, J. (2001). Estimation of uncertain models of activated sludge processes with interval observers. Journal of Process Control, 11(3), 299–310. https://doi.org/10.1016/S0959-1524(99)00074-8
  • Jaulin, L., Kieffer, M., Didrit, O., & Walter, E. (2001). Applied interval analysis: With examples in parameter and state estimation: Robust control and robotics. Springer-Verlag.
  • Jaulin, L., & Walter, E (1993). Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica, 29(4), 1053–1064. https://doi.org/10.1016/0005-1098(93)90106-4
  • J. L. Gouzé, A. R., & Hadj-Sadok, Z. (2000). Interval observers for uncertain biological systems. Ecological Modelling, 133(1-2), 45–56. https://doi.org/10.1016/S0304-3800(00)00279-9
  • Khan, A., Bai, X., Zhang, B., & Yan, P. (2021). Interval state estimator design for parameter varying (LPV) systems. IEEE Transactions on Circuits and Systems, 68(8), 2865–2869. https://doi.org/10.1109/TCSII.2021.3057107
  • Khan, A., Xie, W., & Liu, L. (2020). Set-membership interval state estimator design using the observability matrix for discrete-time switched linear systems. IEEE Sensors Journal, 20(11), 6121–6129. https://doi.org/10.1109/JSEN.7361
  • Khan, A., Xie, W., Zhang, B., & Liu, L. (2021). A survey of interval observes design methods and implementation for uncertain systems. Journal of the Franklin Institute, 358(6), 3077–3126. https://doi.org/10.1016/j.jfranklin.2021.01.041
  • Kieffer, M., & Walter, E. (2004). Guaranteed nonlinear state estimator for cooperative systems. Numerical Algorithms, 37(1-4), 187–198. https://doi.org/10.1023/B:NUMA.0000049466.96588.a6
  • Krebs, S., Meslem, N., & Hohmann, S. (2019). Dynamic set-inversion procedure to design interval-based state estimators for discrete-time LPV systems. In IEEE 58th Conference on Decision and Control (CDC) (pp. 3190–3195). Nice, France.
  • Mazenc, F., & Dinh, T. N. (2014). Construction of interval observers for continuous-time systems with discrete measurements. Automatica, 50(10), 2555–2560. https://doi.org/10.1016/j.automatica.2014.08.008
  • Meslem, N., Hably, A., & Raïssi, T. (2023). State and unknown input set-valued estimation for uncertain linear discrete-time systems. Journal of Systems and Control Engineering, 237(4), 571–584. https://doi.org/10.1177/0959651823115
  • Meslem, N., Loukkas, N., & Martinez, J. J. (2017). A luenberger-like interval observer for a class of uncertain discrete-time systems. In Proceedings of the Asian Control Conference (pp. 1–6). Gold Coast.
  • Meslem, N., Martinez, J. J., Ramdani, N., & Besançon, G. (2020). An H∞ interval observer for uncertain continuous–time linear systems. International Journal of Robust and Nonlinear Control., 30(5), 1886–1902. https://doi.org/10.1002/rnc.v30.5
  • Meslem, N., & Prieur, C. (2014). State estimation based on self-triggered measurements. In Proceedings of the 19th IFAC World Congress (pp. 86–91). Cape Town.
  • Meslem, N., & Ramdani, N. (2011). Interval observer design based on nonlinear hybridization and practical stability analysis. International Journal of Adaptive Control and Signal Processing, 25(3), 228–248. https://doi.org/10.1002/acs.v25.3
  • Meslem, N., & Ramdani, N. (2020). A new approach to design set-membership state estimators for discrete-time linear systems based on the observability matrix. International Journal of Control, 93(11), 2541–2550. https://doi.org/10.1080/00207179.2019.1628296
  • Meslem, N., Ramdani, N., & Candau, Y. (2010). Using hybrid automata for set-membership state estimation with uncertain nonlinear continuous-time systems. Journal of Process Control, 20(4), 481–489. https://doi.org/10.1016/j.jprocont.2010.02.001
  • Moore, R. E. (1966). Interval analysis. Prentice-Hall.
  • Rabehi, D., Meslem, N., & Ramdani, N. (2021, March). Finite-gain event-triggered interval observers design for continuous-time linear systems. International Journal of Robust and Nonlinear Control, 31(9), 4131–4153. https://doi.org/10.1002/rnc.5463
  • Raissi, T., Ramdani, N., & Candau, Y. (2004). Set membership state and parameter estimation for systems described by nonlinear differential equations. Automatica, 40(10), 1771–1777. https://doi.org/10.1016/j.automatica.2004.05.006
  • Raïssi, T., Efimov, D., & Zolghadri, A. (2012). Interval state estimation for a class of nonlinear systems. IEEE Transactions on Automatic Control, 57(1), 260–265. https://doi.org/10.1109/TAC.2011.2164820

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