A. Desantis et al., APPROXIMATION OF THE ALGEBRAIC RICCATI EQUATION IN THE HILBERT-SPACE OF HILBERT-SCHMIDT OPERATORS, SIAM journal on control and optimization, 31(4), 1993, pp. 847-874
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.