  This paper studies the robustness of policy iteration in the context of
continuous-time infinite-horizon linear quadratic regulation (LQR) problem. It
is shown that Kleinman's policy iteration algorithm is inherently robust to
small disturbances and enjoys local input-to-state stability in the sense of
Sontag. More precisely, whenever the disturbance-induced input term in each
iteration is bounded and small, the solutions of the policy iteration algorithm
are also bounded and enter a small neighborhood of the optimal solution of the
LQR problem. Based on this result, an off-policy data-driven policy iteration
algorithm for the LQR problem is shown to be robust when the system dynamics
are subjected to small additive unknown bounded disturbances. The theoretical
results are validated by a numerical example.
