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Zbl 0755.34081
Jeong, Jin-Mun
Stabilizability of retarded functional differential equation in Hilbert space. (English)
[J] Osaka J. Math. 28, No.2, 347-365 (1991). ISSN 0030-6126

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

MSC 2000:: *34K35 Functional-differential equations connected with control problems
34G10 Linear ODE in abstract spaces
34K30 Functional-differential equations in abstract spaces

Keywords: retarded functional differential equation; stabilizability; initial value problem; linear operators; Hilbert spaces

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