Sampling-period-independent (SPI) stabilisation of both periodic and aperiodic sampled-data systems using a class of generalised sampled-data hold functions is addressed. It is proved that for this specific class of hold functions, a continuous-time linear system with rank-minimal input matrix and with non-defective eigenvalues on the imaginary axis is SPI-stabilisable if and only if the spectrum of the system is contained in the closed left-half plane. A systematic procedure for constructing suitable state-feedback controllers is also provided. Several examples are finally discussed for illustration.