State Observation and Filtering

  • Vadim I. Utkin
Part of the Communications and Control Engineering Series book series (CCE)


In the previous chapters, the discussion of problems (in particular, eigenvalue allocation in Chap. 7) was based on the assumption that the system state vector is known. In practice, however, only a part of its components or some of their functions may be measured directly. This gives rise to the problem of determination or observation of the state vector through the information on the measured variables. Below, consideration will be given to the problem formulated in this way for the linear time-invariant system
$$\dot x = Ax + Bu,x \in {\mathbb{R}^n},u \in {\mathbb{R}^m},A,B = const.$$
and it will be assumed that one can measure the vector y that is a linear combination of the system state vector components:
$$y = Kx,y \in {\mathbb{R}^1},1\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } 1 < n,K - const.$$


State Vector Noise Intensity Asymptotic Observer System State Vector Luenberger Observer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin, Heidelberg 1992

Authors and Affiliations

  • Vadim I. Utkin
    • 1
  1. 1.Institute of Control SciencesMoscowUSSR

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