Controllability and Controller-Observer Design for a Class of Linear Time-Varying Systems

  • Paresh Date
  • Bujar Gashi


In this paper a class of linear time-varying control systems is considered. The time variation consists of a scalar time-varying coefficient multiplying the state matrix of an otherwise time-invariant system. Under very weak assumptions of this coefficient, we show that the controllability can be assessed by an algebraic rank condition, Kalman canonical decomposition is possible, and we give a method for designing a linear state-feedback controller and Luenberger observer.


Linear time-varying systems Controllablility Kalman canonical structure Stabilisation  Observer 


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© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.The Centre for the Analysis of Risk and Optimisation Modelling Applications (CARISMA), Department of Mathematical SciencesBrunel UniversityUxbridgeUK
  2. 2.Institute of Financial and Actuarial Mathematics (IFAM), Department of Mathematical SciencesThe University of LiverpoolLiverpoolUK

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