APPROXIMATION OF THE ALGEBRAIC RICCATI EQUATION IN THE HILBERT-SPACE OF HILBERT-SCHMIDT OPERATORS

This paper deals with the problem of approximating the infinite-dimensional algebraic Riccati equation, considered as an abstract equation in the Hilbert space of Hilbert-Schmidt operators. Two kinds of approximating schemes are proposed. The first scheme exploits the already established approximability of the corresponding dynamical Riccati equation together with its time convergence toward the steady state. The second method considers a particular sequence of finite-dimensional linear equations whose solutions are proved to converge toward the exact steady-state solution of the original problem.