  We deduce a sufficient condition of the exponential (integral) turnpike
property for infinite dimensional generalized linear-quadratic optimal control
problems in terms of structural properties of the control system, such as
exponential stabilizability and detectability. The proof relies on the analysis
of the exponential convergence of solutions to the differential Riccati
equations to the algebraic counterpart, and on a necessary condition for
exponential stabilizability in terms of a closed range test.
