@article{7dcd57377cba4d66a629878ba4023de7,
title = "Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations",
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.",
keywords = "Continuous-time algebraic Riccati equation, Krylov subspace, LQR optimal control, Projection method",
author = "Liping Zhang and Fan, {Hung Yuan} and Chu, {Eric King wah}",
note = "Funding Information: Part of the work occurred when the first and third authors visited the School of Mathematical Sciences at Fudan University. The first and the second authors were supported by the National Natural Science Foundation, China (Grant 11601484 ) and the Ministry of Science and Technology, Taiwan (Grant #MOST-108-2115-M-003-004) , respectively. Appendix Funding Information: Part of the work occurred when the first and third authors visited the School of Mathematical Sciences at Fudan University. The first and the second authors were supported by the National Natural Science Foundation, China (Grant 11601484) and the Ministry of Science and Technology, Taiwan (Grant #MOST-108-2115-M-003-004), respectively. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",
year = "2020",
month = jun,
doi = "10.1016/j.cam.2019.112685",
language = "English",
volume = "371",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
}