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On Feedback Transformation and Integral Input-to-State Stability in Designing Robust Interval Observers for Control Systems

  • Thach Ngoc Dinh
  • Hiroshi ItoEmail author
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 471)

Abstract

The problem of designing interval observers is addressed for output feedback control of a class of nonlinear systems in this chapter. The framework of integral input-to-state stability is exploited to drive the estimated intervals and the state variables to the origin asymptotically when disturbances converge to zero. Moreover interval observers are tuned with feedback gain. A reduced-order interval observer is proposed, and the flexibility offered by gains in designing observer is related to the existence of reduced-order interval observers. Comparative simulations are given to illustrate the theoretical results.

Keywords

Interval observers Reduced-order observers Nonlinear systems Output feedback control Guaranteed state estimation. 

References

  1. 1.
    Alcaraz-Gonzalez, V., Harmand, J., Rapaport, A., Steyer, J.P., Gonzalez-Alvarez, V., Pelayo-Ortiz, C.: Software sensors for highly uncertain WWTPs: a new approach based on interval observers. Water Res. 36(10), 2515–2524 (2002)CrossRefGoogle Scholar
  2. 2.
    Bernard, O., Gouzé, J.L.: Closed loop observers bundle for uncertain biotechnical models. J. Process Control 14(7), 765–774 (2004)CrossRefGoogle Scholar
  3. 3.
    Dinh, T.N., Mazenc, F., Niculescu, S.-I.: Interval observer composed of observers for nonlinear systems. In: Proceedings of the 13th European Control Conference, pp. 660–665 (2014)Google Scholar
  4. 4.
    Efimov, D., Perruquetti, W., Richard, J.P.: Interval estimation for uncertain systems with time-varying delays. Int. J. Control 86(10), 1777–1787 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Efimov, D., Raissi, T., Chebotarev, S., Zolghadri, A.: Interval state observer for nonlinear time varying systems. Automatica 49(1), 200–205 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gouzé, J.L., Rapaport, A., Hadj-Sadok, M.Z.: Interval observers for uncertain biological systems. Ecol. Modell. 133(1–2), 45–56 (2000)CrossRefGoogle Scholar
  7. 7.
    Ito, H., Dinh, T.N.: Interval observers for nonlinear systems with appropriate output feedback. In: Proceedings of the 2nd SICE International Symposium on Control Systems, pp. 9–14 (2016)Google Scholar
  8. 8.
    Mazenc, F., Bernard, O.: Interval observers for linear time-invariant systems with disturbances. Automatica 47(1), 140–147 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Mazenc, F., Dinh, T.N.: Construction of interval observers for continuous-time systems with discrete measurements. Automatica 50(10), 2555–2560 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Mazenc, F., Dinh, T.N., Niculescu, S.-I.: Robust interval observers and stabilization design for discrete-time systems with input and output. Automatica 49(11), 3490–3497 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Mazenc, F., Niculescu, S.-I., Bernard, O.: Exponentially stable interval observers for linear systems with delay. SIAM J. Control Optim. 50(1), 286–305 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Polyakova, A., Efimov, D., Perruquetti, W.: Output stabilization of time-varying input delay systems using interval observation technique. Automatica 49(11), 3402–3410 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Raissi, T., Efimov, D., Zolghadri, A.: Interval state estimation for a class of nonlinear systems. IEEE Trans. Autom. Control 57(1), 260–265 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Raissi, T., Ramdani, N., Candau, Y.: Bounded error moving horizon state estimation for non-linear continuous time systems: application to a bioprocess system. J. Process Control 15(5), 537–545 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Université de Valenciennes et du Hainaut-CambrésisValenciennes Cedex 9France
  2. 2.Kyushu Institute of TechnologyFukuokaJapan

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