Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Hybrid Observers

  • Daniele CarnevaleEmail author
Living reference work entry

Latest version View entry history

DOI: https://doi.org/10.1007/978-1-4471-5102-9_95-2


In first part two hybrid observer designs for non-hybrid systems are presented. In the second part, recently results available in the literature related to the observability and observer design for different classes of hybrid systems are introduced.


Hybrid systems; Observer design; Observability; Switching systems 
This is a preview of subscription content, log in to check access.


  1. Ahrens JH, Khalil HK (2009) High-gain observers in the presence of measurement noise: a switched-gain approach. Automatica 45(5):936–943MathSciNetCrossRefGoogle Scholar
  2. Babaali M, Pappas GJ (2005) Observability of switched linear systems in continuous time. In: Morari M, Thiele L (eds) Hybrid systems: computation and control. Volume 3414 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 103–117Google Scholar
  3. Balluchi A, Benvenuti L, Benedetto MDD, Vincentelli ALS (2002) Design of observers for hybrid systems. In: Hybrid systems: computation and control, vol 2289. Springer, StanfordGoogle Scholar
  4. Biyik E, Arcak M (2006) A hybrid redesign of Newton observers in the absence of an exact discrete-time model. Syst Control Lett 55(8):429–436MathSciNetCrossRefGoogle Scholar
  5. Branicky MS (1998) Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Control 43(5):475–482MathSciNetCrossRefGoogle Scholar
  6. Carnevale D, Astolfi A (2009) Hybrid observer for global frequency estimation of saturated signals. IEEE Trans Autom Control 54(13):2461–2464MathSciNetCrossRefGoogle Scholar
  7. Forni F, Teel A, Zaccarian L (2003) Follow the bouncing ball: global results on tracking and state estimation with impacts. IEEE Trans Autom Control 58(8):1470–1485MathSciNetzbMATHGoogle Scholar
  8. Goebel R, Sanfelice R, Teel AR (2009) Hybrid dynamical systems. IEEE Control Syst Mag 29:28–93MathSciNetCrossRefGoogle Scholar
  9. Heemels WPMH, Camlibel MK, Schumacher J, Brogliato B (2011) Observer-based control of linear complementarity systems. Int J Robust Nonlinear Control 21(13):1193–1218. Special issues on hybrid systemsGoogle Scholar
  10. Juloski AL, Heemels WPMH, Weiland S (2007) Observer design for a class of piecewise linear systems. Int J Robust Nonlinear Control 17(15):1387–1404MathSciNetCrossRefGoogle Scholar
  11. Khalil HK, Praly L (2013) High-gain observers in nonlinear feedback control. Int J Robust Nonlinear Control 24:993–1015MathSciNetCrossRefGoogle Scholar
  12. Liu Y (1997) Switching observer design for uncertain nonlinear systems. IEEE Trans Autom Control 42(12):1699–1703MathSciNetCrossRefGoogle Scholar
  13. Luenberger DG (1966) Observers for multivariable systems. IEEE Trans Autom Control 11: 190–197CrossRefGoogle Scholar
  14. Martinelli F, Menini L, Tornambè A (2004) Observability, reconstructibility and observer design for linear mechanical systems unobservable in absence of impacts. J Dyn Syst Meas Control 125:549CrossRefGoogle Scholar
  15. Moraal P, Grizzle J (1995) Observer design for nonlinear systems with discrete-time measurements. IEEE Trans Autom Control 40(3):395–404MathSciNetCrossRefGoogle Scholar
  16. Possieri C, Teel A (2016) Structural properties of a class of linear hybrid systems and output feedback stabilization. IEEE Trans Autom Control 62(6):2704–2719MathSciNetCrossRefGoogle Scholar
  17. Prieur C, Tarbouriech S, Zaccarian L (2012) Hybrid high-gain observers without peaking for planar nonlinear systems. In: 2012 IEEE 51st annual conference on decision and control (CDC), Maui, pp 6175–6180Google Scholar
  18. Raff T, Allgower F (2008) An observer that converges in finite time due to measurement-based state updates. In: Proceedings of the 17th IFAC world congress, COEX, South Korea, vol 17, pp 2693–2695Google Scholar
  19. Sassano M, Carnevale D, Astolfi A (2011) Extremum seeking-like observer for nonlinear systems. In: 18th IFAC world congress, Milano, vol 18, pp 1849–1854Google Scholar
  20. Tanwani A, Shim H, Liberzon D (2013) Observability for switched linear systems: characterization and observer design. IEEE Trans Autom Control 58(5): 891–904MathSciNetCrossRefGoogle Scholar
  21. Teel A (2010) Observer-based hybrid feedback: a local separation principle. In: American control conference (ACC), 2010, Baltimore, pp 898–903Google Scholar
  22. Vidal R, Chiuso A, Soatto S, Sastry S (2003) Observability of linear hybrid systems. In: Maler O, Pnueli A (eds) Hybrid systems: computation and control. Volume 2623 of lecture notes in computer science. Springer, Berlin/Heidelberg, pp 526–539Google Scholar
  23. Tornambé A (1992) High-gain observers for nonlinear systems. International Journal of Systems Science 23(9): 1475–1489MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Dipartimento di Ing. Civile ed Ing. InformaticaUniversità di Roma “Tor Vergata”RomaItaly

Section editors and affiliations

  • Francoise Lamnabhi-Lagarrigue
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRSGif-sur-YvetteFrance