An Approximation Theorem for the Algebraic Riccati Equation

For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati operators in case of a previously developed spline approximation scheme for delay systems is established. Finally, convergence of the transfer-functions of the approximating systems is investigated.