Abstract
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 language | English |
|---|---|
| Article number | 112685 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 371 |
| DOIs | |
| Publication status | Published - 2020 Jun |
| Externally published | Yes |
Keywords
- Continuous-time algebraic Riccati equation
- Krylov subspace
- LQR optimal control
- Projection method
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
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Zhang, L., Fan, H. Y., & Chu, E. K. W. (2020). Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations. Journal of Computational and Applied Mathematics, 371, [112685]. https://doi.org/10.1016/j.cam.2019.112685