Equivalent conditions for the solvability of the infinite-dimensional LQ-problem with unbounded input and output operators

Equivalent conditions are presented for the solvability of the infinite-horizon LQ-problem with stability for a class of infinite-dimensional systems with unbounded input and output operators, (Pritchard-Salamon class). These equivalent conditions are given in terms of a nonstandard Riccati equation and a frequency domain inequality, just as in the finite-dimensional case.<>