An explicit expression is derived for the zero-order hold equivalent z transfer function associated with the Laplace transfer function G(p)(s)exp(-(r + alpha)Ts), where T is the sampling period, r is a positive integer dr zero and 0 less than or equal to alpha less than or equal to 1. Vector-matrix generating rules are given for the numerator polynomial N(z, alpha), and structural relations between its coefficients are derived by invoking a ’correspondence principle’. Approximate root locus analysis is given for N(z, alpha) under the assumption that T is chosen so that, for all i = 1,..., n the relation p(i)T much less than 1 is satisfied, where p(i) are the poles of G(p)(s).