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

This paper deals with the problem of approximating the infinite-dimens ional algebraic Riccati equation, considered as an abstract equation i n the Hilbert space of Hilbert-Schmidt operators. Two kinds of approxi mating schemes are proposed. The first scheme exploits the already est ablished approximability of the corresponding dynamical Riccati equati on together with its time convergence toward the steady state. The sec ond method considers a particular sequence of finite-dimensional linea r equations whose solutions are proved to converge toward the exact st eady-state solution of the original problem.