Conventional Sliding Mode Observers

  • Yuri Shtessel
  • Christopher Edwards
  • Leonid Fridman
  • Arie Levant
Part of the Control Engineering book series (CONTRENGIN)


The purpose of an observer is to estimate the unmeasurable states of a system based only on the measured outputs and inputs. It is essentially a mathematical replica of the system, driven by the input of the system together with a signal representing the difference between the measured system and observer outputs. In the earliest observer, attributed to Luenberger, the difference between the output of the plant and the observer is fed back linearly into the observer. However, in the presence of unknown signals or uncertainty, a Luenberger observer is usually (a) unable to force the output estimation error to zero and (b) the observer states do not converge to the system states. A sliding mode observer, which feeds back the output estimation error via a nonlinear switching term, provides an attractive solution to this issue. Provided a bound on the magnitude of the disturbances is known, the sliding mode observer can force the output estimation error to converge to zero in finite time, while the observer states converge asymptotically to the system states. In addition, disturbances within the system can also be reconstructed.


Unknown Input Mode Observer Symmetric Positive Definite Matrix Distribution Matrix Slide Mode Observer 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yuri Shtessel
    • 1
  • Christopher Edwards
    • 2
  • Leonid Fridman
    • 3
  • Arie Levant
    • 4
  1. 1.Department of Electrical and Computer EngineeringUniversity of Alabama in HuntsvilleHuntsvilleUSA
  2. 2.College of Engineering, Mathematics and Physical ScienceUniversity of ExeterExeterUK
  3. 3.Department of Control Division of Electrical EngineeringFaculty of Engineering National Autonomous University of MexicoFederal DistrictMexico
  4. 4.Department of Applied Mathematics School of Mathematical SciencesTel-Aviv UniversityTel-AvivIsrael

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