Krylov subspace methods for discrete-time algebraic Riccati equations

Liping Zhang, Hung Yuan Fan, Eric King Wah Chu

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4 Citations (Scopus)


We apply the Krylov subspace methods to large-scale discrete-time algebraic Riccati equations. The solvability of the projected algebraic Riccati equation is not assumed but is shown to be inherited from the original equation. Solvability in terms of stabilizability, detectability, stability radius of the associated Hamiltonian matrix and perturbation theory are considered. We pay particular attention to the stabilizing and the positive semi-definite properties of approximate solutions. Illustrative numerical examples are presented.

Original languageEnglish
Pages (from-to)499-510
Number of pages12
JournalApplied Numerical Mathematics
Publication statusPublished - Jun 2020


  • Discrete-time algebraic Riccati equation
  • Inheritance property
  • Krylov subspace
  • LQR optimal control
  • Projection methods

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