@article{0239d55b14394dc1bca907be95bdd215,
title = "Perturbation analysis of the stochastic algebraic Riccati equation",
abstract = "In this paper we study a general class of stochastic algebraic Riccati equations (SARE) arising from the indefinite linear quadratic control and stochastic H∞ problems. Using the Brouwer fixed point theorem, we provide sufficient conditions for the existence of a stabilizing solution of the perturbed SARE. We obtain a theoretical perturbation bound for measuring accurately the relative error in the exact solution of the SARE. Moreover, we slightly modify the condition theory developed by Rice and provide explicit expressions of the condition number with respect to the stabilizing solution of the SARE. A numerical example is applied to illustrate the sharpness of the perturbation bound and its correspondence with the condition number.",
author = "Chiang, {Chun Yueh} and Fan, {Hung Yuan} and Lin, {Matthew M.} and Chen, {Hsin An}",
note = "Funding Information: The authors wish to thank the editor and two anonymous referees for many interesting and valuable suggestions on the manuscript. This research work is partially supported by the National Science Council and the National Center for Theoretical Sciences in Taiwan. The first author was supported by the National Science Council of Taiwan under Grant NSC 102-2115-M-150-002. The second author was supported by the National Science Council of Taiwan under Grant NSC 102-2115-M-003-009. The third author was supported by the National Science Council of Taiwan under Grant NSC 101-2115-M-194-007-MY3. Publisher Copyright: {\textcopyright} 2013 Chiang et al.",
year = "2013",
doi = "10.1186/1029-242X-2013-580",
language = "English",
volume = "2013",
journal = "Journal of Inequalities and Applications",
issn = "1025-5834",
publisher = "Springer Publishing Company",
number = "1",
}