Fast projection methods for minimal design problems in linear system theory

S. Kung, T. Kailath

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


The so-called minimal design problem (or MDP) of linear system theory is to find a proper minimal degree rational matrix solution of the equation H(z)D(z)=N(z), where {N(z),D(z)} are given p×r and m×r polynomial matrices with D(z) of full rank r≦m. We describe some solution algorithms that appear to be more efficient (in terms of number of computations and of potential numerical stability) than those presently known. The algorithms are based on the structure of a polynomial echelon form of the left minimal basis of the so-called generalized Sylvester resultant matrix of {N(z), D(z)}. Orthogonal projection algorithms that exploit the Toeplitz structure of this resultant matrix are used to reduce the number of computations needed for the solution.

Original languageEnglish (US)
Pages (from-to)399-403
Number of pages5
Issue number4
StatePublished - Jul 1980
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Control and Systems Engineering


  • Linear Systems
  • fast algorithms
  • minimal realization
  • multivariable systems
  • projection methods


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