On the disturbance rejection for sampled-data discrete-time linear systems

The problem of asymptotic tracking and disturbance rejection for known classes of disturbance functions and reference signals has been investigated by many authors, both for continuous-time and discrete-time linear plants. For sampled-data systems, the asymptotic tracking can be taken into account through an appropriate class of discrete-time reference signals, obtained as the sequence of samples of the continuous-time signals. However, it is unclear how to obtain an appropriate class of discrete-time disturbances for which the corresponding state and output responses of the discrete-time sampled-data system coincide with the state and output responses of the continuous-time plant at the sampling instants. In this context, the main object is to solve the following problem: given a continuous-time plant which is subject to disturbances belonging to a given class, find, if any, a discrete-time description for the corresponding sampled-data system, including discrete-time disturbances, for which the state and output responses coincide with those of the original continuous-time plant at the sampling instants