U-D factorisation of the strengthened discrete-time optimal projection equations

L. Gerard Van Willigenburg*, Willem L. De Koning

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


Algorithms for optimal reduced-order dynamic output feedback control of linear discrete-time systems with white stochastic parameters are U-D factored in this paper. U-D factorisation enhances computational accuracy, stability and possibly efficiency. Since U-D factorisation of algorithms for optimal full-order output feedback controller design was recently published by us, this paper focusses on the U-D factorisation of the optimal oblique projection matrix that becomes part of the solution as a result of order-reduction. The equations producing the solution are known as the optimal projection equations which for discrete-time systems have been strengthened in the past. The U-D factored strengthened discrete-time optimal projection equations are presented in this paper by means of a transformation that has to be applied recursively until convergence. The U-D factored and conventional algorithms are compared through a series of examples.

Original languageEnglish
Pages (from-to)1032-1041
Number of pages10
JournalInternational Journal of Systems Science
Issue number5
Publication statusPublished - 2016


  • compensatability and optimal compensation
  • multiplicative white noise
  • optimal reduced-order controller design
  • stochastic parameters
  • systems with state and control-dependent noise
  • UDU factorisation

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