A New Methodology of Judging the Observability of the System

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 107)


The controllability and observability of a linear system are the two basic concepts of linear system, in order to judge the observability of linear system: \( \left\{ \begin{gathered} \dot{x}(t) = Ax(t) + Bu(t) \hfill \\ y(t) = Cx(t) \hfill \\ \end{gathered} \right. \), this chapter bring forward a form of matrix decomposition through primary transform, and thus come up with a new methodology of judging the observability of linear system.


Primary transform Matrix decomposition Linear system observability 


  1. 1.
    Hom RA, Johnson CR (1991) Topics in matrix analysis [M]. The Cambridge University, New YorkGoogle Scholar
  2. 2.
    Wei M, Wang Q, Cheng X (2010) Some new result for system decoupling and pole assignment problems [J]. Automatica 46:937–944CrossRefMATHGoogle Scholar
  3. 3.
    Wei M, Cheng X, Wang Q (2010) A Canonical decomposition of the right invertible system with application[J]. Slam J Matrix Anal Appl 31(4):1958–1981CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Zheng D (1990) The theory of linear system (M). Tsinghua University Press, Beijing, (1933.3), (Chinese)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Mathematics and Applied Mathematics School of Mathematics and Information of Ludong UniversityYantaiPeople’s Republic of China

Personalised recommendations