@article{3941fd113a2c4ef29dce83c242ef5afc,

title = "Krylov subspace methods for discrete-time algebraic Riccati equations",

abstract = "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.",

keywords = "Discrete-time algebraic Riccati equation, Inheritance property, Krylov subspace, LQR optimal control, Projection methods",

author = "Liping Zhang and Fan, {Hung Yuan} and Chu, {Eric King Wah}",

note = "Funding Information: Part of the work was done when the third author visited the School of Mathematical Sciences at Fudan University. The first and the second authors were supported by the National Natural Science Foundation , People's Republic of China (Grant 11601484 ) and the Ministry of Science and Technology, Taiwan (Grant # MOST-107-2115-M-003-003 ), respectively. Funding Information: Part of the work was done when the third author visited the School of Mathematical Sciences at Fudan University. The first and the second authors were supported by the National Natural Science Foundation, People's Republic of China (Grant 11601484) and the Ministry of Science and Technology, Taiwan (Grant #MOST-107-2115-M-003-003), respectively. Publisher Copyright: {\textcopyright} 2019 IMACS",

year = "2020",

month = jun,

doi = "10.1016/j.apnum.2019.11.006",

language = "English",

volume = "152",

pages = "499--510",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier",

}