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Stabilizability of retarded functional differential equation in Hilbert space. (English) Zbl 0755.34081
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.

##### MSC:
 34K35 Control problems for functional-differential equations 34G10 Linear differential equations in abstract spaces 34K30 Functional-differential equations in abstract spaces