It is known that if a continuous-time feedback system is exponentially stable, then the corresponding sampled-data system obtained by sample-hold discretisation with constant sampling period is also exponentially stable, provided that the sampling period tau > 0 is sufficiently small. In general, it is difficult to estimate how small the sampling period has to be in order to achieve the stability of the sampled-data system. In this article, we present an adaptive mechanism for adjusting the sampling period. This mechanism has the properties that, for every initial state, (i) the adaptation of the sampling period terminates after finitely many time steps and (ii) the state of the adaptive sampled-data system is integrable and converges to zero as time goes to infinity.