TY - JOUR

T1 - Residual bounds of the stochastic algebraic Riccati equation

AU - Chiang, Chun Yueh

AU - Fan, Hung Yuan

N1 - Funding Information:
We gratefully thank the editor and two anonymous referees for their helpful comments and suggestions that substantially improve this article. The first author would like to thank the support from National Science Council in Taiwan under grant number NSC100-2115-M-150-001.

PY - 2013/1

Y1 - 2013/1

N2 - In this paper we consider a class of continuous-time algebraic Riccati equations with a constraint of positive definiteness, which occurs in the indefinite stochastic linear quadratic control problems and stochastic H ∞ control problems, respectively. The normwise local and non-local residual bounds are derived for a symmetric solution which approximates the unique stabilizing solution to the stochastic algebraic Riccati equation. A numerical example is presented to illustrate the sharpness of ours residual bound.

AB - In this paper we consider a class of continuous-time algebraic Riccati equations with a constraint of positive definiteness, which occurs in the indefinite stochastic linear quadratic control problems and stochastic H ∞ control problems, respectively. The normwise local and non-local residual bounds are derived for a symmetric solution which approximates the unique stabilizing solution to the stochastic algebraic Riccati equation. A numerical example is presented to illustrate the sharpness of ours residual bound.

KW - A posteriori error bound

KW - Forward error

KW - Residual bound

KW - Stabilizing solution

KW - Stochastic algebraic Riccati equations

UR - http://www.scopus.com/inward/record.url?scp=84868693969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868693969&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2012.09.007

DO - 10.1016/j.apnum.2012.09.007

M3 - Article

AN - SCOPUS:84868693969

SN - 0168-9274

VL - 63

SP - 78

EP - 87

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -