Editing State observer (section)

=== Peaking and other observer methods ===

When the observer gain <math>L</math> is high, the linear Luenberger observer converges to the system states very quickly. However, high observer gain leads to a peaking phenomenon in which initial estimator error can be prohibitively large (i.e., impractical or unsafe to use).<ref name="Khalil02">{{Citation
 | last = Khalil
 | first = H.K.
 | authorlink = Hassan K. Khalil
 | year = 2002
 | edition = 3rd
 | url = http://www.egr.msu.edu/~khalil/NonlinearSystems/
 | isbn = 978-0-13-067389-3
 | title = Nonlinear Systems
 | publisher = [[Prentice Hall]]
 | location = Upper Saddle River, NJ}}</ref> As a consequence, nonlinear high-gain observer methods are available that converge quickly without the peaking phenomenon. For example, [[sliding mode control]] can be used to design an observer that brings one estimated state's error to zero in finite time even in the presence of measurement error; the other states have error that behaves similarly to the error in a Luenberger observer after peaking has subsided. Sliding mode observers also have attractive noise resilience properties that are similar to a [[Kalman filter]].<ref name="UtkinGS99">{{citation|title=Sliding Mode Control in Electromechanical Systems|last1=Utkin|first1=Vadim|last2=Guldner|first2=Jürgen|last3=Shi|first3=Jingxin|year=1999|publisher=Taylor & Francis, Inc.|location=Philadelphia, PA|isbn=978-0-7484-0116-1}}</ref><ref name="Drakunov83">{{citation|title=An adaptive quasioptimal filter with discontinuous parameters|journal=Automation and Remote Control|last1=Drakunov|first1=S.V.|year=1983|volume=44|issue=9|pages=1167–1175}}</ref>
Another approach is to apply multi observer, that significantly improves transients and reduces observer overshoot. Multi-observer can be adapted to every system where high-gain observer is applicable.<ref name="MMObserver">{{citation|doi=10.1080/00207179.2014.1000380|bibcode=2015IJC....88.1209B|title=Multi modelling as new estimation schema for High Gain Observers|journal=International Journal of Control|last1=Bernat|last2=Stepien |first1=J.|first2=S.|year=2015|volume=88|issue=6|pages=1209–1222|s2cid=8599596}}</ref>