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
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U2 - 10.1016/j.apnum.2012.09.007
DO - 10.1016/j.apnum.2012.09.007
M3 - Article
AN - SCOPUS:84868693969
VL - 63
SP - 78
EP - 87
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
ER -