Time-varying linear systems

  • Zeitvariante Lineare Systeme

Belayneh, Berhanu Bekele; Zerz, Eva (Thesis advisor)

Aachen : Publikationsserver der RWTH Aachen University (2007)
Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2007


The main goal of this thesis is to examine linear dynamical systems, both in the continuous- and discrete-time case, with time-varying coefficients using module theory and homological methods and to generalize results, such as the realization problem and matrix fraction descriptions, from the time-invariant case to the time-varying case. After a short introduction to behavioral systems theory we briefly describe the mathematical background of the algebraic approach. We then study structural properties such as autonomy, controllability, and observability. A realization problem of time-varying systems specified by a transfer matrix is also addressed. It is shown that realizability is equivalent to properness and minimality is equivalent to both controllability and observability. The notions of coprimeness of a matrix fraction description and row-properness of a skew polynomial matrix are introduced and used to determine the size of a minimal realization. An algorithm to transfer a given skew polynomial matrix into row-proper form is given and it is used to compute one sided greatest common divisors and least common multiples.


  • Department of Mathematics [110000]
  • Mathematics (Algebra) Teaching and Research Area [114920]