Smith method for projected Lyapunov and Stein equations

Bo Yu, Hung Yuan Fan, Eric King Wah Chu

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


We consider the projected Lyapunov and Stein equations arising in model order reduction and optimal control of descriptor systems. The projected Lyapunov equation is transformed to an equivalent projected Stein equation then solved by a generalized Smith iterative method. For a projected general Stein equation with a singular matrix "E", a double Cayley transform is devised to remove the singularity, and then the generalized Smith method is applied. Numerical examples are provided to demonstrate the feasibility and efficiency of our approach.

Original languageEnglish
Pages (from-to)191-204
Number of pages14
JournalPolytechnical University of Bucharest Scientific Bulletin Series A: Applied Mathematics and Physics
Issue number2
Publication statusPublished - 1 Jan 2018


  • Cayley transform
  • Descriptor system
  • Double Cayley transform
  • Projected Lyapunov equation
  • Projected Stein equation

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