Some aspects of the continuity of the stationary Riccati equation in Hilbert space

In adaptive control and other problems in control it is important to know that the solution of the stationary Riccati equation for a linear regulator control problem is a continuous function of parameters. Although this result is well known for finite-dimensional linear regulator control problems, it has not been previously verified for infinite-dimensional linear regulator problems in the form that is required for adaptive control. Specifically, it is shown in this study that the symmetric, nonnegative solution of the stationary Riccati equation in Hilbert space is a continuous function of parameters in the uniform operator topology.<>