Stabilization of Linear Continuous Time-Varying Systems with State Delays in Hilbert Spaces
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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.
CitationPhat, V. N. (2001). Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces. Electronic Journal of Differential Equations, 2001(67), pp. 1-13.
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