Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 67, pp. 1-13.

Title: Stabilization of linear continuous time-varying systems
       with state delays in Hilbert spaces
   
Author: Vu Ngoc Phat (Univ. of New South Wales, Australia)
         
Abstract:  
 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.

Submitted August 16, 2001. Published October 19, 2001.
Math Subject Classifications: 93D15, 93B05, 34K20.
Key Words: Stabilization; time-varying; delay system; Riccati equation.