Can continuous-time disturbance be represented by sampled input disturbance?

In this paper, we study whether any continuous-time disturbance to a continuous-time plant can be equivalently represented by a sampled input disturbance to a sampled-data model. With the help of the sampled-data system theory, we show that such equivalent sampled disturbance exists for almost sampling period and even for mismatched continous-time disturbances. Moreover, it is also discussed that whether the equivalent sampled disturbance is bounded significantly depends on the zeros of the sampled-data system. Simulation results verify the validity of the stability analysis.