Stabilization of Linear Continuous Time-Varying Systems with State Delays in Hilbert Spaces

Abstract

This 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.