Stabilization of periodic systems with aftereffect by finite-dimensional approximations

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We study the stabilization problem for a linear periodic system of differential equations with aftereffect. Approximating systems are described by differential equations with finite-dimensional Volterra operators. We construct admissible controls in the class of piecewise continuous functions by the feedback principle. We establish a connection between the approximating stabilization problem and that of the optimal stabilization for an autonomous linear system of difference equations.