Geodesic
Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces
Electronic journal of differential equations, Tome 2001 (2001)
This paper studies the stabilization of the infinite-dimensional linear time-varying system with state delays

$\dot x = A(t)x + A_1(t)x(t-h)+B(t)u\,.$

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.
Classification : 93D15, 93B05, 34K20
Keywords: stabilization, time-varying, delay system, Riccati equation 
@article{EJDE_2001__2001__a111,
     author = {Vu Ngoc Phat},
     title = {Stabilization of linear continuous time-varying systems with state delays in {Hilbert} spaces},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {1020.93017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a111/}
}
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Vu Ngoc Phat. Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a111/