Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations

Liping Zhang, Hung Yuan Fan, Eric King wah Chu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We investigate the theory behind the Krylov subspace methods for large-scale continuous-time algebraic Riccati equations. We show that the solvability of the projected algebraic Riccati equation need not be assumed but can be inherited. This study of inheritance properties is the first of its kind. We study the stabilizability and detectability of the control system, the stability of the associated Hamiltonian matrix and perturbation in terms of residuals. Special attention is paid to the stabilizing and positive semi-definite properties of approximate solutions. Illustrative numerical examples for the inheritance properties are presented.

Original languageEnglish
Article number112685
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 2020 Jun


  • Continuous-time algebraic Riccati equation
  • Krylov subspace
  • LQR optimal control
  • Projection method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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