In this paper, a method to construct complete rational orthonormal model sets with prescribed asymptotic order is presented for continuous-time systems. Two special cases that illustrate the application of the method are studied. In the first case, this method is shown to produce the generalized Laguerre functions which form a complete model set for H-2 and have asymptotic order two. In both eases, this method is equivalent to calculating Toeplitz determinants generated by a rational function. The latter problem is reduced to finding solution of a linear finite-difference equation.