This paper studies the problem of robust stabilization of an infinite dimensional plant by a stable and possibly low order controller. The plant of interest is assumed to have only finitely many simple unstable zeros, however, may have infinitely many unstable poles. In the literature, it has been shown that the problem can be reduced to an interpolation problem and it is possible to obtain lower and upper bounds of the multiplicative uncertainty under which an infinite dimensional stable controller can be generated by a modified Nevanlinna-Pick formulation. We propose that the same interpolation problem can be solved approximately by a finite dimensional approach and present a finite dimensional interpolation function which can be used to find a stable controller. We illustrate this idea by a numerical example and additionally show the effects of the free design parameters of the rational interpolating outer function approach on the numerical example.