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This paper studies the prescribed-time input-to-state stabilization problem of normal nonlinear systems. With the help of some key properties of a class of parametric Lyapunov equations, the prescribed-time input-to-state stabilization problem of normal nonlinear systems under matched uncertainties is studied. Some bounded time-varying controllers are proposed. It is shown that the closed-loop systems are prescribed-time input-to-state stable. Finally, the effectiveness of the established methods is illustrated by two physical systems.