On the Sensitivity of Solutions of Riccati Equations to Small Parameter Perturbations and Optimality in Linear Stochastic Control Systems

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