Stabilization of infinite-dimensional linear dynamical systems by the Kalman-Letov method (Q1060175)

The linear-quadratic control problem in Hilbert space is considered. Exponential stabilizability of the control system is not supposed. Under weak controllability assumptions the solvability of the corresponding algebraic operator Riccati equation in the class of self-adjoint (generally unbounded) operators is proved. The stabilizing solution \(K_ 0\) of this equation is used to construct a feedback providing the evolution of the closed-loop system within \(D(K_ 0)\) (domain of \(K_ 0)\). The corresponding control appears to be optimal in the class of all \(L^ 2\)-controls.