Abstract: Due to the fact that many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed, this paper deals with the differentiability of the Pritchard-Salamon system with admissible state-feedback. Spectrum analysis showed that under definite condition, the unbounded perturbation semigroup of the Pritchard-Salamon system is eventually differentiable.

Key words: C₀-semigroup, Differentiability, Admissible operator, Pritchard-Salamon systems, Perturbation

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