Jeong, Jin-Mun Stabilizability of retarded functional differential equation in Hilbert space. (English) Zbl 0755.34081 Osaka J. Math. 28, No. 2, 347-365 (1991). 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. Reviewer: T.Havarneanu (Iaşi) Cited in 13 Documents MSC: 34K35 Control problems for functional-differential equations 34G10 Linear differential equations in abstract spaces 34K30 Functional-differential equations in abstract spaces Keywords:retarded functional differential equation; stabilizability; initial value problem; linear operators; Hilbert spaces PDF BibTeX XML Cite \textit{J.-M. Jeong}, Osaka J. Math. 28, No. 2, 347--365 (1991; Zbl 0755.34081)