In this paper we study the balancing and model-reduction of linear sys
tems with discrete jumps at periodic time instants. These systems aris
e in the study of linear systems with sampled data control and filteri
ng problems. We study the balancing for the case of fixed and infinite
intervals. We show that the system balancing can be used to obtain a
reduced order-model of the system with the properties of the original
system. An example is provided to illustrate the procedure.