Stabilizability of retarded functional differential equation in Hilbert space (Q1191041)

The author establishes a necessary and sufficient condition in order that the following initial value problem is stabilizable: \({d\over dt}u(t)=A_ 0u(t)+\int^ 0_{-h}a(s)A_ 1u(t+s)ds+\varphi_ 0f(t)\), \(u(0)=g^ 0\), \(u(s)=g^ 1(s)\), \(s\in[-h,0)\), where \(A_ 0,A_ 1,\varphi_ 0\) are linear operators defined on certain Hilbert spaces.