A fast algorithm to solve Kalman’s partial realisation problem for single input, multi-output systems

  • P. R. Graves-Morris
  • J. M. Wilkins
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1287)


A brief review is given of the solution of the scalar partial realisation problem using Padé approximants. The use of simultaneous Padé approximants in the solution of the single input, multi-output partial realisation problem is then discussed. We show how analogues of Frobenius identities are derived for simultaneous Padé approximants of two series, and we give twelve such identities. We show how some of these identities are combined to construct analogues of Baker’s and Kronecker’s algorithms. These analogues are fast algorithms for simultaneous Padé approximation of two series, and so also for a solution of the single input, two output partial realisation problem.


Single Input Degree Reduction Reliable Algorithm Markov Parameter Denominator Polynomial 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • P. R. Graves-Morris
    • 1
  • J. M. Wilkins
    • 2
  1. 1.School of Mathematical SciencesUniversity of BradfordBradfordEngland
  2. 2.D.A.M.T.P.Cambridge UniversityCambridgeEngland

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