LQ-optimal actuator location and norm convergence of Riccati operators

In many problems governed by partial differential equations, there is freedom in the choice of actuator (and sensor) location. These locations should be chosen to optimize performance objectives. In practice, approximations are used in controller design and thus in selection of the actuator locations. The optimal cost and location of the approximating sequence should converge to the exact optimal cost and location. In this work conditions for this convergence are given in the case of linear quadratic control.