Two main goals are to discretise the solution of an autonomous linear singular continuous-time system and to compare the discretised with the continuous solution at fixed time moments. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena. The complex Kronecker canonical form decomposes the singular system into five sub-systems, whose solutions are obtained. Moreover, in order for the norm of the difference between the two solutions to be smaller than a fully pre-defined, acceptable bound, the sampling period should be arranged in a particular interval. A numerical example is also available.