Phat, Vu Ngoc2020-07-022020-07-022001-10-19Phat, V. N. (2001). Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces. <i>Electronic Journal of Differential Equations, 2001</i>(67), pp. 1-13.1072-6691https://hdl.handle.net/10877/11944This paper studies the stabilization of the infinite-dimensional linear time-varying system with state delays ẋ = A(t)x + A1(t)x(t - h) + B(t)u. The operator A(t) is assumed to be the generator of a strong evolution operator. In contrast to the previous results, the stabilizability conditions are obtained via solving a Riccati differential equation and do not involve any stability property of the evolution operator. Our conditions are easy to construct and to verify. We provide a step-by-step procedure for finding feedback controllers and state stability conditions for some linear delay control systems with nonlinear perturbations.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalStabilizationTime-varyingDelay systemRiccati equationArticle