Residual bounds of the stochastic algebraic Riccati equation

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.