A numerical algorithm for reconstructing continuous-time linear models with pure integrators from their discrete-time equivalents

A numerical algorithm for reconstructing continuous-time linear models with pure integrators from their discrete-time equivalents is derived in this paper. The algorithm treats the reconstruction problem in the frequency-domain and establishes a numerically tractable z-domain to s-domain mapping, which avoids the need to software packages with symbolic mathematical solving capabilities. The proposed algorithm can be conveniently implemented using standard building block numerical routines and has been recently employed in a computer-aided control systems design software package. Unlike other approaches, this algorithm is shown to avoid unnecessary computations, which typically result in numerical burden, ambiguity, and singularity. A numerical example is illustrated demonstrating the application of the proposed algorithm.