On the Sensitivity of Solutions of Riccati Equationsto Small Parameter Perturbations and Optimality in Linear Stochastic ControlSystems

We study the sensitivity of solutions of Riccati equations to asymptotically small perturbations of their coefficients. An upper bound on the difference between the solutions of algebraic and differential Riccati equations is derived. The result is applied to study optimality in a stochastic linear-quadratic control problem over an infinite time horizon for an asymptotically autonomous system. We also study the performance of an invariant control strategy.