Observability of Linear Differential-Algebraic Systems: A Survey

Part of the Differential-Algebraic Equations Forum book series (DAEF)


We investigate different concepts related to observability of linear constant coefficient differential-algebraic equations. Regularity, which, loosely speaking, guarantees existence and uniqueness of solutions for any inhomogeneity, is not required in this article. Concepts like impulse observability, observability at infinity, behavioral observability, strong and complete observability are described and defined in the time-domain. Special emphasis is placed on a normal form under output injection, state space and output space transformation. This normal form together with duality is exploited to derive Hautus-type criteria for observability. We also discuss geometric criteria, Kalman decompositions and detectability. Some new results on stabilization by output injection are proved.


Controllability Differential-algebraic equations Duality Hautus Test Kalman decomposition Observability Output injection Wong sequences 

Mathematics Subject Classification (2010)

93B07 34A09 93B10 93B25 93B27 93B05 93C05 



We thank the referees of this article for their valuable comments which very much helped to improve the manuscript.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität HamburgHamburgGermany
  2. 2.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany

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