The continuization of a discrete process and applications in interpolation and multi-rate control

The inverse problem of the discretization for a linear system is solved. It is shown that an nth-order discrete system can always be “continuized” by a minimal real system of order between n and 2n. Applications to Lyapunov equations equivalence and certain interpolation methods are given. This is of independent interest in multi-rate control systems, especially when the rates are not commensurate.