Uniform operator continuity of the stationary Riccati equation in Hilbert space

Abstract

In this paper the continuity in the uniform operator topology of the solution of the stationary Riccati equation in Hilbert space as a function of parameters is verified. The assumptions for this verification are the uniform operator continuity of the uncontrolled semigroup with respect to parameters, the uniform finiteness of the infimum of the quadratic cost functionals over the admissible controls, and uniform detectability. Some families of semigroups are described that satisfy the condition of continuity in the uniform operator topology with respect to parameters. The uniform operator continuity of the solution of the stationary Riccati equation with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.