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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
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